JEE Main 2024 Mathematics question
If α denotes the number of solutions of |1 − i|ˣ = 2ˣ and , where , i = √−1, then the distance of the point (α, β) from the line 4x – 3y = 7 is .
Answer: 3
Solution
|1 − i|ˣ = (√2)ˣ = 2ˣ has the single solution x = 0, so α = 1. Each fraction in the bracket simplifies to −i (multiply by the conjugate of the denominator), so the bracket
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