For any two complex numbers z1, z2 and a, b∈R. |az1+bz2|2+|bz1−az2|2=
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a
(a2+b2) (|z1|2+|z2|2)
b
(a2−b2) (|z1|2−|z2|2)
c
a2+b2
d
none of these
answer is A.
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Detailed Solution
We have|az1+bz2|2+|bz1−az2|2=|az1|2+|bz2|2+2Re(az1 bz2¯) +|bz1|2+|az2|2−2Re(bz1 az2¯)=a2|z1|2+b2|z2|2+2abRe(z1 z¯2) + b2|z1|2+a2|z2|2−2abRe(z1 z2¯) [∵ a and b are real numbers]=(a2+b2) (|z1|2+|z2|2)