JEE Main 2024 Mathematics question
Let the complex number α and lie on the circles |z – z₀|² = 4 and |z – z₀|² = 16 respectively, where z₀ = 1 + i. Then, the value of 100|α|² is .
Answer: 20
Solution
With |z₀|² = 2, the conditions become |α|² − αz̄₀ − z₀ᾱ − 2 = 0 (1) and, for 1/α (using 1/α = ᾱ/|α|²), 1 − αz̄₀ − z₀ᾱ − 14|α|² = 0 (2). Subtracting (1) from (2):
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