We've built this powers of i calculator so that you can easily and effortlessly compute every power of the imaginary unit. How to use the tool? Just input the power n that you need to evaluate and the result will appear immediately!

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Oct 19, 2023 · What Is I Raised To The Power I? An imaginary number raised to an imaginary number turns out to be real. However, while learning complex analysis, one learns that an exponential with respect to an imaginary number does not have a single, fixed value.

The newer TI-84+CE will give an exact answer ( i, 1, -i -1) up to a power of 100. Beyond these powers, the calculators will give an estimate (in scientific notation) that will need to be interpreted as to whether the answer is i, 1, -i , or -1.

Aug 8, 2023 · Before calculating i to the power i, it is worth looking at i raised to a real power, as this will give us a couple of insights into the problem. We can calculate i squared like this: This value has a unit length and an angle of π radians (half a full turn). This makes it equal to -1.

Mar 6, 1997 · I am interested in knowing what i to the power of i is. The first question to address is what it means to raise one complex number to the power of another. There is a basic definition of what it means to raise e to a complex power, as described in the answer to an earlier question .

The imaginary unit i is defined as the square root of − 1 . So, i 2 = − 1 . i 3 can be written as ( i 2 ) i , which equals − 1 ( i ) or simply − i . i 4 can be written as ( i 2 ) ( i 2 ) , which equals ( − 1 ) ( − 1 ) or 1 . i 5 can be written as ( i 4 ) i , which equals ( 1 ) i or i .

The value of i is equal to root of minus of one. Learn to derive the value of the power of i like square, i cube, etc. here with the help of solved examples and table at BYJU'S.

It is a rather curious fact that i raised to the i-th power is actually a real number! In fact, its value is approximately 0.20788. This makes a great exercise after learning the basics about complex numbers. From Euler’s formula, we know that exp (i*x) = cos (x) + i*sin (x), where “exp (z)” is the exponential function ez. Then.

But i^i is a real number, approximately equal to 0.208. Why is this true? It is an incredibly tricky calculation if you want to justify the steps properly. All of the videos I've seen on...