Question

All the values of the multi-valued complex function $1^i$, where $i=\sqrt{-1}$

• A. are purely imaginary
• B. have same real and imaginary parts
• C. are real and non-negative
• D. lie on a unit circle

Answer 1

The correct option is C are real and non-negative

$1^i=(\cos 2n\pi +i\sin 2n\pi {)}^i=(e^{i2n\pi }{)}^i=e^{-2n\pi }$
which is always real and non-negative.