The least positive integer n such that `(2i/(1+i))^n` is a positive integer is :

Explanation

`2i=2e^(pi/2)`

`(2i/(1+i))^n=((2e^(pi/2))/sqrt2e^(pi/4))`

`=sqrt2e^(pi/4)`

`A=sqrt2^ne^(i npi/4)`

If n=4

`A=sqrt2^4e^(ipi)=-sqrt2^4`

if n=8

`A=sqrt2^8 e^(i2pi)=sqrt2^8`

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