Question

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

Answer 1

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

Explanation:

In general, for any given `z_0 in CC`,
`|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`

`=> |z - (-1 + i)| = 2`

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