Let z = a + ib, b 0 be complex numbers satisfying z^ 2 = z̄·2^ 1−|z| . Then the least value of n N, such that z^ n = (z + 1)^ n , is equal to _____.

JEE Main 2022 Mathematics question

Let z = a + ib, be complex numbers satisfying = z̄·. Then the least value of n N, such that , is equal to .

Answer: 6

From = z̄·, taking moduli gives = |z|·, so |z| = and |z| = 1 ( since ). Then = z̄ gives z̄ = 1, so z = −1/2 , a primitive cube root

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Question ID VK-034713