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Question

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

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 D 0
|z|=|w|=k where k>0
z=k(cosA+isinA)&w=k(cosB+isinB)
α=z¯wk2+z¯w
Re(α)=α+¯α2=12(z¯wk2+z¯w+¯zwk2+w¯z)
Re(α)=12⎜ ⎜zk2+w|z|2¯wk2¯z|w|2+¯zk2+¯w|z|2wk2z|w|2(k2+z¯w)(k2+w¯z)⎟ ⎟=12⎜ ⎜zk2+wk2¯wk2¯zk2+¯zk2+¯wk2wk2zk2(k2+z¯w)(k2+w¯z)⎟ ⎟
Re(α)=0
Ans: A

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