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Question

For any two complex numbers z1z2 and any two real numbers a and b |az1−bz2|2+|bz1+az2|2 =


A

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B

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C

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D

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Solution

The correct option is B


|az1−bz2|2+|bz1+az2|2

= (az1−bz2)(a¯¯¯¯¯z1−b¯¯¯¯¯z2)+(az1+bz2)(a¯¯¯¯¯z1+b¯¯¯¯¯z2)

= a2z1z2+b2z2¯¯¯¯¯z2−abz1¯¯¯¯¯z2−abz2¯¯¯¯¯z1+b2z1¯¯¯¯¯z1+a2z2¯¯¯¯¯z2+abz1¯¯¯¯¯z2+abz2¯¯¯¯¯z1

= (a2+b2)(|z1|2+|z2|2) ∴ z ¯¯¯z = |z|2


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