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Prove that z=i^i ,w h e r ei=sqrt(-1) , ...

Prove that `z=i^i ,w h e r ei=sqrt(-1)` , is purely real.

Text Solution

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`z = i^(i) = (cos.(pi)/(2) + i sin .(pi)/(2))^(i) = (e^(ipi//2))^(i) = e^(-(pi)/(2))`
`rArr Re(z) = e^(-(pi)/(2))`
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