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If z=(i)^(i)^(((i)))w h e r e i=sqrt(-1)...

If `z=(i)^(i)^(((i)))w h e r e i=sqrt(-1),t h e n|z|` is equal to `1` b. `e^(-pi//2)` c. `e^(-pi)` d. none of these

A

1

B

`e^(-pi//2)`

C

`e^(-pi)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
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`
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