sathya76 wrote:

||z|-2| = z-1

Squaring both sides

|z|^2 - 4|z| + 4 = z^2 - 2z + 1

Since |z|^2 = z^2 we get

-4|z| + 4 = -2z + 1

4|z| = 2z + 3

Again squaring both sides

16z^2 = 4z^2 + 12z + 9

ie 4z^2 - 4z - 3 = 0

Solving for Z we get z = -1/2 or z = 3/2

But when choices are given, checking by substitution will be easier than this long process.

-1/2 is clearly out. When you square an equation, you can get many extraneous roots. Therefore, each root should be plugged to make sure that it does make sense.