[JEE Advanced 1988] For any complex $z_1,z_2$ and reals $a,b$: $|az_1-bz_2|^2+|bz_1+az_2|^2=$ ____
For any complex $z_1,z_2$ and reals $a,b$: $|az_1-bz_2|^2+|bz_1+az_2|^2=$ ____
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo ago
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Answer: $(a^2+b^2)(|z_1|^2+|z_2|^2)$.
Expanding both moduli, the cross terms cancel, leaving $(a^2+b^2)(|z_1|^2+|z_2|^2)$.
JEE Advanced 1988 · Complex Numbers — verified solution by the Vidaara Team.
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