Powers of complex numbers

Calculus Level 3

Fill in the blank:

The number i i i^i is _____________ . \text{\_\_\_\_\_\_\_\_\_\_\_\_\_} .

Clarification: i 2 = − 1 , i = − 1 i^2= -1, i = \sqrt { -1 } .

Solve with this link, logarithms of complex numbers.

a rational number an irrational number. a strictly imaginary number neither a real nor strictly complex number

. . by . . , 14, South Korea

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2 solutions

. .
Feb 17, 2021

For that link, it says that i i \displaystyle i ^ { i } is equal to e − π 2 \displaystyle e ^ { - \frac { \pi } { 2 } } . So it is a real number.

1 Helpful 1 Interesting 1 Brilliant 1 Confused
Sk Kumar
Feb 22, 2021

lnz =i lni lnz=-π/2

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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