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1. Let \( z_{1}, z_{2} \in C \) such that \( \left|z_{1}+z_{2}\right|=\sqrt{3} \) and \( \left|z_{1}\right|=\left|z_{2}\right|=1 \) then thevalue of \( \left|z_{1}-z_{2}\right| \) is |
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Answer» We have |z1 + z2| = √3 and |z1| = |z2| = 1 ∵ |z1 + z2|2 + |z1 - z2|2 = 2(|z1|2 + |z2|2) ⇒ |z1 - z2|2 = 2(|z1|2 + |z2|2) - |z1+z2|2 = 2(1+1) - 3 (∵ |z1| = |z2| = 1 and |z1 + z2| = √3) = 4 - 3 = 1 |
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