Question

Let z and w be two complex numbers such that |z| ≤ 1, |w| ≤ 1 and |z + iw | = |z - i bar w | = 2,then z equals

(a)1 or i

(b) 1 or -i

(c) 1 or -1

(d) i or -1

Answer 1

The correct option is (c) 1 or -1

Explanation:

∴ z lies on the perpendicular bisector of the line joining -iw and -i bar w. since - i bar w is the  mirror image of -iw in the x-axis, the locus of z is the x-axis.