Lösung 3.2:2d

In general, the expression \displaystyle |z-w| is equal to the distance between the complex numbers \displaystyle z and \displaystyle w, so if we rewrite the equality in the exercise as

\displaystyle |z-(1+i)|=3

it says that the distance between \displaystyle z and \displaystyle 1+i should be \displaystyle 3, i.e. we obtain a circle of radius \displaystyle 3 and centre at \displaystyle 1+i.