# What does the curve from the equation |z+1-i| = 2 look like in the complex plane?

##### 1 Answer
Dec 28, 2015

The curve is a circle of radius $2$ centered at $- 1 + i$.

#### Explanation:

In general, for any given ${z}_{0} \in \mathbb{C}$,
$| z - {z}_{0} | = r$ is a circle of radius $r$ centered at ${z}_{0}$.

This should make sense intuitively, as $| z - {z}_{0} |$ may be interpreted as the distance between $z$ and ${z}_{0}$. The locus of points a fixed distance from a given point is a circle centered at that point with that distance as the radius.

For the given equation, then

$| z + 1 - i | = 2$

$\implies | z - \left(- 1 + i\right) | = 2$

Thus the curve is a circle of radius $2$ centered at $- 1 + i$.