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Question

If z and α complex numbers such that |z|=|α|=r,r>0 and ω=z¯¯¯¯αr2+z¯¯¯¯α, find Re(ω).

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Solution

|z=|α|=r
z=a1+ib1 z=a21+b21=ra21+b21=a22+b22
x=a2+ib2 x=a22+b22=r a21a22=b22b21
w=a1+ib1a2ib2r2+a1a2b1b2a1a2+ib1ib2r2+a1a2b1b2
Re(w)=a1a2r2+a1a2b1b2
a21+b21 or a22+b22

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