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Find the least positive integer n such t...

Find the least positive integer `n` such that `((2i)/(1+i))^n` is a positive integer.

A

n =6

B

n =5

C

n =8

D

n =4

Text Solution

Verified by Experts

The correct Answer is:
C
`((2i)/(1+i))+((2i(1-i))/((1+i)(1-i)))^(n)= ((2(i-i^(2)))/(2)))^(n)`
`= (i+1)^(n)`
`=(2i)^(n//2)`
Hence , n= 8 is the least positive interger for which the given complex number is a positive integer.
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