# Thread: region represented complex no/ problem

1. ## region represented complex no/ problem

find the region represented by |z-4| < |z-2|, where z is a complex number.

my incomplete soln-
don't have any idea about it.

2. Originally Posted by saha.subham
find the region represented by |z-4| < |z-2|, where z is a complex number.

my incomplete soln-
don't have any idea about it.
|z-4|<|z-2|
Have you drawn a graph to help? Hint: Consider the lines $x=2$, $x=3$ and $x=4$

3. Write $\displaystyle z = x + iy$, where $\displaystyle x, y \in \mathbf{R}$ and simplify.