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Question

The smallest positive integer n for which (1+i)2n=(1i)2n is

A
4
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B
8
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C
2
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D
12
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Solution

The correct option is C 2
We have,
(1+i)2n=(1i)2n
(1+i1i)2n=1
((1+i)(1+i)12i2)2n=1
(1+i2+2i2)2n=1
(2i2)2n=1
i2n=1

For smallest positive integer i4=1
n=2

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