JEE Main 2022 Mathematics question
Let S = {z ℂ : |z − 3| and z(4 + 3i) + z̄(4 − 24}. If is the point in S which is closest to 4i, then is equal to .
Answer: 80
Solution
|z − 3| is the closed disc with centre (3, 0) and radius 1. With z = x + iy, z(4 + 3i) + z̄(4 − , i.e. , the half-plane through the centre (3, 0). The
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