1.

If z=i^("ii") where i=sqrt(-1), then |z| is equal to :

Answer»

1
`E^(-pi//2)`
`e^(-pi)`
NONE of these

Solution :`i=cos.(pi)/(2)+isin.(pi)/(2)=(ipi)/(e^(2))`
`rArr i^(i)=(e^((IX)/(2)))^(i)=e^(-(pi)/(2))`
`rArr z=(i)^((i)^(i))=1^(.e^(-(pi)/(2)))`
`rArr|z|=1`


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