Let w be a complex number with 0 < |w| < 1. Show that the set of all z with these properties is as described

1: Show that |z - w| < |1 - w*z| is the disc {z:|z| < 1}

2: Show that |z - w| = |1 - w*z| is the circle {z:|z| = 1}

3: Show that |z - w| > |1 - w*z| is the circle {z:|z| > 1}

I squared both sides and simplified... assuming that it would equal

a^2 + b^2 < 1

given z= a +bi and w= c + di

but i got

a^2 + b^2 + c^2 + d^2 - (a^2)(c^2) - (b^2)(c^2) - (b^2)(d^2) -(a^2)(d^2) < 1

which i simplified to...

(|z|^2)(1 - (|w|^2)) + |w|^2 < 1

anyone know what i am doing wrong?