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Question

Let z1 and z2 be complex numbers, then |z1+z2|2+|z1z2|2 is equal to

A
|z1|2+|z2|2
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B
2(|z1|2+|z2|2)
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C
2(z21+z22)
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D
4z1z2
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Solution

The correct option is C 2(|z1|2+|z2|2)
|z1+z2|2=|z1|2+|z2|2+2Re(z1¯z2)
|z1z2|2=|z1|2+|z2|22Re(z1¯z2)
|z1+z2|2+|z1z2|2=2(|z1|2+|z2|2)

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