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Question

If z1,z2 are complex numbers, then the maximum value of z1¯z2+¯z1z2+z1z2+¯z1¯z2|z1z2| is equal to

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Solution

z1=r1eiθ1,z2=r2eiθ2

z1¯z2+¯z1z2+z1z2+¯z1¯z2|z1z2|=2 cos(θ1θ2)+2cos(θ1+θ2)4


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