Let's start from the begginning.

We have the equation :

As recommended by Mr Penrose, we first verify this equation multiplying on both sides with c+id :

Then we develop separating reals and complex :

And there we are, with :

Now the other part of the exercise is not as quick as this one but still interesting :

But now we can use the relation :

So we can rewrite the previous equality as :

And we find :

This is a final equality, because we can get it explaining the left hand side or simplifying the right hand side.