Q25 of 66 Page 91

Fill in the blanks of the following

For any two complex numbers z1, z2 and any real numbers a, b, |az1 – bz2|2 + |bz1 + az2|2 = ….

Given |az1 – bz2|2 + |bz1 + az2|2


= |az1|2 + |bz2|2 – 2 Re (az1 × bz̅ 2) + |bz1|2 + |az2|2 + 2 Re (bz1 × az̅ 2)


= (a2 + b2) |z1|2 + (a2 + b2) |z2|2


= (a2 + b2) (|z1|2 + |z2|2)bz = |


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