Question

If `z=(i)^{(i)^(i)} w h e r e i=sqrt(-1),t h e n|z|` is equal to
A. 1
B. `e^(-pi//2)`
C. `e^(-pi)`
D. none of these

Answer 1

Correct Answer - A
`i=cos.(pi)/(2)+isin.(pi)/(2)=e^((ipi)/(2))`
`rArr i^(i)=(e^((ipi)/(2)))^(i)=e^((pi)/(2))`
`rArrz=(i)^("(i)"^(i))=i^(e^(-(pi)/(2)))`
`rArr |z|=1`