# How do you sketch the set of all the complex numbers z such that |z- 3- 4i| = 2?

Dec 23, 2015

This will be a circle of radius $2$ centred on $3 + 4 i$

#### Explanation:

graph{((x-3)^2+(y-4)^2 - 4)((x-3)^2+(y-4)^2-0.003) = 0 [-9.5, 10.5, -1.36, 8.64]}

If ${z}_{1}$ and ${z}_{2}$ are Complex numbers, then $\left\mid {z}_{1} - {z}_{2} \right\mid$ is the distance between ${z}_{1}$ and ${z}_{2}$.

So we can read $\left\mid z - 3 - 4 i \right\mid = 2$ as "the distance between $z$ and $3 + 4 i$ is $2$".