Q:

Solving abs equations with complex solution

I want to solve equations containing absolute values for complex solutions. Eg: $$|x+2| - 7 = 0$$ has real solution as $\{-9, 5\}$ and complex solution as $\{-2 + 7\mathrm{e}^{\mathrm{i}θ}\}$. Real solutions can be easily derived but how do I get complex solutions?
Also can I get some references where there is an explanation for this.
Thanks in advance.

A:

$$|x+2|-7=0$$ means
$$|x-(-2)|=7$$
It is a circle centered at $(-2,0)$ with radius $7$.
$$x=-2+7\exp(i \theta), \theta \in [0, 2\pi)$$

