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Question

If k>0,z=w=k and α=z¯¯¯¯wk2+z¯¯¯¯w, then Re(α) equals

A
0
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B
k2
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C
k
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D
None of these
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Solution

The correct option is A 0
α=z¯¯¯¯wk2+z¯¯¯¯w¯¯¯¯α=¯¯¯zwk2+¯¯¯zw
But z¯¯¯z=w¯¯¯¯w=k2. Hence,
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯α=k2zk2¯¯¯¯wk2+k2zk2¯¯¯¯w=¯¯¯¯wzz¯¯¯¯+k2=α
α+¯¯¯¯α=0
Re(α)=0

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