For each \(x\in\mathbb C\), \(x\neq 0\), there exists a number \(x^{-1}\in\mathbb C\) with \(x\cdot x^{-1}=1\).
In particular, the inverse of $x\neq 0$ can be calculated using the formula $$\frac 1x=\frac{\Re(x)-\Im(x)}{|x|^2}$$
In the following interactive figure, you can experiment with the value of \(x\) (i.e. its position in the complex plane) and see, how it influences the value of \(x^{-1}\), the inverse complex number with respect to multiplication:
Proofs: 1
Proofs: 1