Lösung 3.1:4a

A general strategy when solving equations is to try to get the unknown variable by itself on one side.

In this case, we start by subtracting z from both sides,

z+3i−z=2z−2−z

Then we have a z left on the right-hand side,

3i=z−2.

We add 2 to both sides to remove the −2 from the right hand side

3i+2=z−2+2

and after that we can just read off the solution:

2+3i=z

To check that we have calculated correctly, we substitute z=2+3i into the original equation and see that it is satisfied:

LHSRHS=z+3i=2+3i+3i=2+6i=2z−2=2(2+3i)−2=4+6i−2=2+6i