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Question

If z=(3+4i)6+(34i)6, where i=1, then Im(z) equals to

A
6
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B
0
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C
6
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D
None of these
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Solution

The correct option is A 0
z=(3+4i)6+(34i)6
=[5(eiθ)]6+[5(eiθ)]6 [where θ=tan1(4/3)]
=56[ei6θ+ei6θ]
=56[2Re(ei6θ)]
In (z)=0 [B]

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