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Question

If (3i)n=2n, nϵZ, then n is multiple of

A
6
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B
10
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C
9
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D
12
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Solution

The correct option is B 12
(3i)n=2n
(2.eiπ6)n=2n
2neinπ6=2n
2n(einπ61)=0
Since 2n0,
Hence
einπ61=0
einπ6=1
einπ6=ei2kπ where k=±1,±2,±3..
nπ6=2kπ
n=12k
Hence n is a multiples of 12.

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