Raising to imaginary powers!

Algebra Level 4

Which of the following is a possible value of the complex exponentiation:

$\large {\color{#20A900}{1}^{\color{#3D99F6}{i}}} ?$

e^{i}

e^{i\pi}

-e^{i\pi}

\log_{i}{e^{\pi}}

None of these.

1 solution

Will McGlaughlin
Apr 25, 2018

${ 1 }^{ x }$ is always equal to one regardless of what x is.

Therefore the solution to ${ 1 }^{ i }=1$

${ e }^{ i\pi }=-1$

therefore $-{ e }^{ i\pi }=1$

$\boxed{-{ e }^{ i\pi }}$

Why does e↑(iπ)=−1?

Allen Helmer - 1 year, 10 months ago