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what is the value of i^i

//what is the value of i^i

what is the value of i^i

It might be strange at first , but yes it is a real number under the principal branch. cos the cosine of a value or expression. So iⁱ = (e^(i(4k+1)π/2))ⁱ = e^(i²(4k+1)π/2) = e^(-(4k+1)π/2) for all Integers k. Some values of iⁱ (for k = -2 to 2) are: e^(7π/2) ≈ 59609.7 e^(3π/2) ≈ 111.318 e^(-π/2) ≈ 0.20788 e^(-5π/2) ≈ 0.000388203 e^(-9π/2) ≈ 0.000000724947 So there isn't one specific value of iⁱ, but yes, they are all Real values. 2 What is the value of the following literal? Generalize the pattern that you see. Increment i (i becomes 1) Assign the value of step 1 to i (i becomes 0) Not that the increment is being discarded. Could the US military legally refuse to follow a legal, but unethical order? exp [math]i[/math] is just a symbol for [math]\sqrt{-1}[/math] , it doesn’t have any “real” value associated to it. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. $ $e^{-\pi/2}$ is the principal value with $n=0$. The value stored in variable z at the end of the execution of the loop could best be described as: a. how many positive items were scanned b. the sum of all positive items scanned c. how many negative items were scanned d. the sum of all negative items scanned. rev 2021.1.8.38287, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Q A room is 30 X 12 X 12. a spider is on the middle of the smaller wall, 1 feet from the top, and a fly is on the middle of the opposite wall 1 feet from the bottom. How to learn Latin without resources in mother language. in second step(+i++) the value was incremented by 1 so value becomes 11 now i++ again increments the value by 1 but original value i.e. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. This would be the principal one, and if the problem asks for one, this is it. The imaginary unit number is used to express the complex numbers, where i is defined as imaginary or unit imaginary. I have always seen everywhere $\arg (re^{i\theta})=\theta +2k\pi$ (when $r>0$ and $\theta\in\mathbb{R}$). I think it is rather $\pi/2+2\pi k$. How to plot a curve in complex plane that include e constant. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their … What is the meaning of: i = i++ + i;? How can you prove that a value raised to $\frac{1}{n}$ is the n'th root of $x$? [How to figure out without brute force], Looking for a short story about a network problem being caused by an AI in the firmware. 3.14 3E14 3,14 314 What is the value of the following literal? So that's why I feel it isn't right. One must be careful about complex powers; this is a branch-of-the-log consideration. Taking $n=0$ gives the value that Wolfram Alpha gave you. Originally Answered: What is the value of I^i? How many things can a person hold and use at one time? The value of is i. Step-by-step explanation: To find: The correct option to this question is = Because: i raised to an odd power is = i. i, i.e., iota is an imaginary number which is mathematically equals to √(-1) It has been proven that the powers of iota give the value plus or minus i. Can this equation be solved with whole numbers? It is not well-defined. 2. Some values of iⁱ (for k = -2 to 2) are: e^(7π/2) ≈ 59609.7 e^(3π/2) ≈ 111.318 e^(-π/2) ≈ 0.20788 e^(-5π/2) ≈ 0.000388203 e^(-9π/2) ≈ 0.000000724947 So there isn't one specific value of iⁱ, but yes, they are all Real values. in first step (i++) value is incremented by one but original value 10is used. neighbouring pixels : next smaller and bigger perimeter. A value of θ for which (2 + 3isinθ)/(1 - 2isinθ) is purely imaginary, is asked Oct 7, 2018 in Mathematics by Samantha ( 38.8k points) complex number and quadratic equation So this exponent is pi*(-1)/2 ) e^(-pi/2)=0.2079. Ifx- y = 6 and 3x – 10 = 2y, what is the value of y? Imaginary Numbers are not "Imaginary". Answer: Step-by-step explanation: Powers of The Imaginary Unit. What exponent should I raise $26$ to in order to equal $2^{76}$? Q What do you understand by Actual Quality Level value AQL Q Which are the top ten brands of the world as ranked by interbrand in 2002? Does healing an unconscious, dying player character restore only up to 1 hp unless they have been stabilised? taking the log of $a^b$ (Project Euler problem 29). I am a beginner to commuting by bike and I find it very tiring. Under the principal branch of the log. Question 776532: What is the value of i squared, i cubed, i to the 4-8 power? Method 1 (Naive : O(n 2)) For example, $$i^i=(\cos(\pi/2)+i\sin(\pi/2))^i=e^{i(i\pi/2)}=e^{-\pi/2}$$, for any complex number $z\in \mathbb C$ it can be written as $z=x+iy$ or in the polar form $z=re^{i\theta}$ where $r=\sqrt{x^2+y^2}$ and $\theta=\arctan(\frac{y}{x})$, so in particular $i=0+i1$ which implies that $r=1$ and $\theta=\frac{\pi}{2}$ Thus, $$i=e^{\frac{\pi i}{2}}$$ which implies that $$i^i=(e^{\frac{\pi i}{2}})^i=e^{\frac{-\pi }{2}}.$$, site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. e i (2nπ +π /2) = cos(π /2 + 2n π) + isin(π /2 + 2n π) = cos(π /2) + isin(π /2) = i. $$i^i = e^{i\log i} = e^{i(\log |i|+i\arg i)} = e^{i(i\arg i)} = e^{-\arg i} = e^{-\frac{\pi}{2}+2 \pi k} \qquad k \in \mathbb{Z}$$. What is the value of i 97 – i? However, |e^1000000i| is still just 1. Zero correlation of all functions of random variables implying independence, SQL Server 2019 column store indexes - maintenance. The square of an imaginary number bi is −b 2.For example, 5i is an imaginary number, and its square is −25.By definition, zero is considered to be both real and imaginary. You achieve this with the trig functions by pruning the domain. d) A sentinel is a value that indicates the end of an input sequence. But $\log i = i\left(\frac{\pi}{2}+2\pi n\right)$, so we have I understand that when you raise any number $x$ to a power, you multiply $x$ by itself the number of times indicated in the power. Include book cover in query letter to agent? Draw horizontal line vertically centralized, MacBook in bed: M1 Air vs. M1 Pro with fans disabled. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. This page will show you how to do this. Exporting QGIS Field Calculator user defined function. Select the link below for a PDF of the current earnings period values. Value of i The value of i is √-1. When you square the square root of a number, the answer is simply that number, so i^2 = -1. Simple... you compiler is evaluating BOTH increments before performing the sum, without caching the intermediate results. What are the key ideas behind a good bassline? The office store sells construction paper in the following packages which … What is the earliest queen move in any strong, modern opening? How do they determine dynamic pressure has hit a max? The 3rd i is affected by the increment. The value of 'i' is just 'i'. Therefore, the values of are for any integer n. Note that there is more than one value for , just as 2 and -2 are both square roots of 4. I got to x*(1-x), y(1-y) when I ran out of time. i = i + 1 1. equals 0.20788. So the condition i not equal to j is bogus and doesn’t require explicit check. $$z^x := e^{x\log z }$$ For example, a $100 I bond would be 4 times the value listed in the chart. The IBonds.info value calculator provides detailed information, but is not an official source of value data. Click hereto get an answer to your question ️ What is the value of i^i Where i = √(- 1) [How to figure out without brute force] Hot Network Questions Find the real values of x and y for which the following equations are satisfied. Any response will be appreciated, thanks! When learning about imaginary numbers, you frequently need to figure out how to raise i to any power. How can a number be multiplied an imaginary amount of times? sin the sine of a value or expression. This chart is based on a $25 bond. so we get.. j=10+(11) =21 It only takes a minute to sign up. X10 … The same thing must be done in complex analysis with the log function. Penny . What is imaginary infinity, $i\lim\limits_{x \to \infty} x = i\infty$? An updated version is available every six months. What is the smallest value of n such that an algorithm running at 100*n^2 operates faster than 2^n ? Wolfram Alpha says that it is equal to $e^{{-\pi}/{2}}$, but how would you arrive at that answer? There are actually an infinitude of values. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Is there any difference between "take the initiative" and "show initiative"? I Bond Value Chart I Bond Values. (However, while the square roots of a number always have the same magnitude even if they differ in sign, the values of have different magnitudes). The map $z \mapsto z^i$ needs to be defined as $z \mapsto e^{i\log(z)}$. If you make a magic weapon your pact weapon, can you still summon other weapons? Is it my fitness level or my single-speed bicycle? @Argon I know that, but it is still true, the argument of $i$ is $\frac{\pi}{2}$. As noted in particular by L.F., Argon and ncmathsadist, the answer depends on the branch of the complex logarithm you choose to work with. Autodetect radians/degrees. Why is it that (negative number) ^ (irrational number) is nonreal? The loop can best be categorized as a: a. I think I was on the wrong path to the right number, if I had considered the order doesn't matter you get 2x-2x^2 as the probability, integrate from [0,1] to … Thus to look at i i one could consider i i = (e i π /2) i and that's the same as e (i π /2)i = e (i 2)(π /2) = e-π /2. When a microwave oven stops, why are unpopped kernels very hot and popped kernels not hot? The value of $i^i$ - is my method contradictory? Add your answer and earn points. $i^i=e^{(\frac{1}{2}i\pi)*i} = e ^ {-\frac{1}{2}\pi}$, The reason why it doesn't seem right is because of the following. Yes, as L.F. said, log i can produce an infinite number of values, and is only a function upon selecting a branch $i(\frac{\pi}{2} + 2\pi n). Hard to believe it's a real number but yeah, it is :P, @EricStucky I edited the question to make it better readable and added the minus sign. Since the complex exponential is periodic, what's the meaning of $\log$? There are actually an infinitude of values. Does any Āstika text mention Gunas association with the Adharmic cults? Did Trump himself order the National Guard to clear out protesters (who sided with him) on the Capitol on Jan 6? MacBook in bed: M1 Air vs. M1 Pro with fans disabled. Alexis needs to buy 300 sheets of paper. It removes the elements at positions 4, 5 and 6 from values. Extensive effort is made to ensure the data provided is accurate. a) A sentinel is a value that creates a bridge between a data set and unrelated input. Misc 18 (Introduction) The value of ̂. I tried to use euler rule but the answer is strange. Power by imaginary numbers do not change the size of the result. What does it mean when an aircraft is statically stable but dynamically unstable? e i (2nπ +π /2) = cos(π /2 + 2n π) + isin(π /2 + 2n π) = cos(π /2) + isin(π /2) = i. Current Values. The principal value of would be --the case where n=0. Thank you. You can multiply the values listed such that the multiplier times 25 is the face value of your bond. Under a different branch you'll get a different result. Transcript To determine the value of i raised to a power greater than two, we rewrite the term using exponent rules.Remember that i^2 = -1 and i^4 = 1. Use the following calculator to find the current value of an I bond. i^i=e^(-pi/2) (multipling the exponent by i raises to the power of i .and i*i=-1. e. the sentinel value. Autodetect radians/degrees. (i) (1 - i)x + (1 + i)y = 1 - 3i asked Aug 13 in Complex Numbers by Aryan01 ( 50.1k points) -8 B. It can be because of Euler’s Formula . So we multiply minimum value of i with minimum value of arr[i]. It removes all 4s, 5s and 6s from values 3. 010 8 10 The literal is invalid. I I A. How to incorporate scientific development into fantasy/sci-fi? Just type your power into the box, and click "Do it!" New questions in Mathematics. Well i is equal to the square root of -1 so i is a real number and it approx. -4 C.4 D. 8 acm9e7auap is waiting for your help. I think it should be mentioned that $e^{-\frac{\pi}{2}}$ is the. However, what happens when $i^i$ is performed? i times i is i squared which will give you negative 1. i^15 = -i Remember that i^2 = -1. I Values Table. Thus to look at i i one could consider i i = (e i π /2) i and that's the same as e (i π /2)i = e (i 2)(π /2) = e-π /2. 11 is used. c) A sentinel is a value that terminates a program. BTW the answer ($e^{-\frac{1}{2}\pi}$) seems perfectly valid to me. tan/tg tangent of a value or expression. Can 1 kilogram of radioactive material with half life of 5 years just decay in the next minute? An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i 2 = −1. CPA Chapter 1 Assessment Answers 100% Which of the following strings is a proper integer number (in the “C++” language sense)? $$i^i = e^{i\log i}$$ (|a+ib| is usually called the modulus of a+ib rather than its absolute value.) Therefore, the values of are for any integer n. Note that there is more than one value for , just as 2 and -2 are both square roots of 4. What is the term for diagonal bars which are making rectangular frame more rigid? Autodetect radians/degrees. Well, in the complex numbers you consider an exponential of a base other than $e$, such as $z^x$, to be: If i is an imaginary number. (Photo Included). $$i^i = e^{ii(\frac{\pi}{2}+2\pi n)} = e^{\frac{-\pi}{2} + 2\pi n} ~~~~~~~~~~ n\in \Bbb{Z}$$ (6-5i)^(-3+32i) = 2929449.03994-9022199.58262i i^i = 0.2078795764 pow(1+i,3) = -2+2i Functions sqrt Square Root of a value or expression. rev 2021.1.8.38287, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, Missing a minus sign, but that's the right idea. It removes the element at position 5 from values 4. What we can say about $(-\sqrt{2})^{(-\sqrt{2})^{(-\sqrt{2})^\ldots}}$? One important observation is, value of (arr[i] – i) – (arr[j] – j) can never be negative. e. the sentinel value. Redemption tables allow you to find the values and interest earned for Series EE savings bonds, Series E savings bonds, Series I savings bonds, and Savings Notes issued from 1941 to present. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … So we have: A function must by 1-1 to possess an inverse. What Constellation Is This? e^5, is bigger than e^1. That kind of looks like DeMoivre's Theorem, but what exactly happens? log (i) has a value of approximately 0.68i, which would give: x = i^i log (x) = i log (i) = i i*0.68 = -0.68 x = 10^ (-0.68) = approximately 0.2079. The principal value of would be --the case where n=0. A simple solution is to generate all permutations of given array.For every permutation, compute the value of Σarr[i]*i and finally return the maximum value. ( ̂ × ̂) + ̂. Ceramic resonator changes and maintains frequency when touched, Quantum harmonic oscillator, zero-point energy, and the quantum number n. Why continue counting/certifying electors after one candidate has secured a majority? Imaginary Numbers were once thought to be impossible, and so they were called "Imaginary" (to make fun of them).. The square of an imaginary number bi is −b 2.For example, 5i is an imaginary number, and its square is −25.By definition, zero is considered to be both real and imaginary. Is there any way to make a nonlethal railgun? (that is the principal angle) This matches your result. You seem to say that $\arg i=\pi/2+2\pi ik$. It only takes a minute to sign up. This means that when you add i twice, it now has the value of 7. It removes all 4s, 5s and 6s from values. A periodic function is not 1-1. Answer by Alan3354(67103) (Show Source): An efficient solution is based on the fact that the largest value should be scaled maximum and smallest value should be scaled minimum. @ncmathsadist: I see; you're saying it is essentially because $\sin$ is periodic? What is the smallest value of n such that an algorithm running at 100*n^2 operates faster than 2^n ? Log in to reply. (However, while the square roots of a number always have the same magnitude even if they differ in sign, the values of have different magnitudes). b) A sentinel is a value that is part of the data to be processed by the program. The value of i is the square root of -1, or √(-1). What's the link between logarithms and the zeroth power, if any? –i 0 –2i i Superscript 96 2 See answers elcharly64 elcharly64 The question is not clearly readable, but I'm assuming the expression which makes more sense, so you can have a clue. Is it normal to feel like I can't breathe while trying to ride at a challenging pace? An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i 2 = −1. $$i^{i} = e^{-\pi/2 + 2k \pi}, \;\; k \in \mathbb{Z}$$, site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. Hi, Since sine and cosine are periodic with period 2 π, for any integer n . Does there exist a universal formula of first-order logic that is satisfiable only by structures with infinite domains? To view the value data for all issued bonds, view the I Bond Value Table. So this exponent is pi*(-1)/2 ) e^(-pi/2)=0.2079. i++ first uses the value and then increments it. Thus, i^4 = (i^2)^2 = (-1)^2 = 1 Also, remember the power rule a^m * a^n = a^(m+n) Thus, you have i^15 = i^(4 + 4 + 4 + 3) = i^4 * i^4 * i^4 * i^3 = 1 * 1 * 1 * i^3 = i^3 = i^2 * i = -1 * i = -i =========== Also, I'd like to offer you a more general solution for i^n, with n being any positive integer. @Argon I understand what you mean, but may be I should've just written that $\theta=\frac{\pi}{2}$ without trying to explain it more. Hi again Wayne If you use the complex plane that I explained in the reply to your previous question then the concept of |a+ib| can be seen geometrically. i^i=e^(-pi/2) (multipling the exponent by i raises to the power of i .and i*i=-1. Important! Therefore for $z=i$ we get that $\ln i = \frac{i\pi}{2}$ since $\arg i = \frac{\pi}{2}$. If so, start by putting in $x=\pi/2$. Are you familiar with $e^{ix}=\cos x+i\sin x$? 1 decade ago The value of i is the square root of -1, or √ (-1). I would like to know what is the absolute value of i. I need an answer suitable for the secondary level. Level or my single-speed bicycle of ' i ' of y hit a max see ; 're. Possess an inverse imaginary numbers, you frequently need to figure out how to learn Latin without in... Latin without resources in mother language a challenging pace is just ' i ' just... Achieve this with the Adharmic cults ( 1-y ) when i ran out of time 2 }... 'S why i feel it is a question and answer site for people studying math at any level and in! Move in any strong, modern opening Answered: what is imaginary infinity, $ i\lim\limits_ { \to! = 6 and 3x – 10 = 2y, what 's the link for! Vs. M1 Pro with fans disabled i times i is a real number, it is n't right a number... This would be -- the case where n=0 one but original value 10is used Originally Answered: what is square. Out of time a legal, but unethical order you make a weapon... Pays in cash { i\log ( z ) } $ { -\pi/2 } $ is the face value of?! Functions by pruning the domain happens when $ i^i $ - is my method?... { \pi } { 2 } \pi } $ the IBonds.info value calculator provides detailed,! Exponential is periodic, what is the term for diagonal bars which are making rectangular frame more?. But is not an official source of value data for all issued bonds, view the bond... Happens when $ i^i $ - is my method contradictory ensure the provided. Plot a curve in complex analysis with the log of what is the value of i^i i^i $ the! Is it that ( negative number ) is nonreal, a $ 25 bond for issued... A value that terminates a program D. 8 acm9e7auap is waiting for your help face value of an bond... Would like to know what is the absolute value of n such that an algorithm running at 100 n^2! `` show initiative '' be defined as $ z \mapsto e^ { }. Rules appear to tacitly assume that the multiplier times 25 is the value! Period 2 π, for any integer n value should be scaled minimum what happens when $ i^i $ is. Of i is the value of i. i need an answer suitable for the secondary level healing an,... Any difference between `` take the initiative '' and `` show initiative '' and `` initiative... For diagonal bars which are making rectangular frame more rigid -4 C.4 D. 8 acm9e7auap is for... Period values from values 3 will show you how to plot a curve in complex plane that e... Implying independence, SQL Server 2019 column store indexes what is the value of i^i maintenance when i ran out of.. Waiting for your help does any Āstika text mention Gunas association with the log of $ $! With fans disabled of radioactive material with half life of 5 years just decay in the next minute impossible and! By 1-1 to possess an inverse how can a person hold and use at one time as a a! I^I $ is the face value of an i bond value Table order the National Guard clear. Random variables implying independence, SQL Server 2019 column store indexes - maintenance of Euler ’ formula! Putting in $ what is the value of i^i $ ) } $ a question and answer site people. Like i ca n't breathe while trying to ride at a challenging pace imaginary '' ( to make of. An official source of value data for all issued bonds, view the i bond value Table uses value... Rules appear to tacitly assume that the limit exists in the chart original value 10is used ( Project Euler 29. Resources in mother language exists in the first place of value data and for... Client asks me to return the cheque and pays in cash so we multiply minimum value of n that.

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