Let z and w be non-zero complex numbers such that z w = z 2 and z - z - + w + w - = 4 . If w varies, then the perimeter of the locus of z is

Question

Let z and w be non-zero complex numbers such that z w = z 2 and z - z - + w + w - = 4 . If w varies, then the perimeter of the locus of z is, 8 2 units, 4 2 units, 8 units, 4 units

MARKS App · Accepted Answer

Given, z w = z 2 ⇒ z w = z z - ⇒ w = z - z ≠ 0 Now, z - z - + w + w - = 4 ⇒ z - z - + z + z - = 4 Let, z = x + i y , then we get, x + y = 2 which represents a square of side length equal to 2 2 ⇒ The perimeter of the locus is 8 2 units

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