How to find all solutions of $e^z = 2020(-1 + i)$ in rectangular coordinates

Question

How do I find all solutions of $e^z = 2020(-1 + i)$ (in rectangular coordinates)?

This is what I have so far:

$e^z = e^x \cos(y) + e^x \sin(y)i$

so $e^x \cos(y) = -2020$ and $e^x \sin(y) = 2020$.

No idea how to continue from here.

Answer 1

Note,

$$e^z = 2020(-1 + i)=2020\sqrt2 e^{i\frac{3\pi}4+i2\pi n}$$

Then, the solutions are,

$$z= \ln(2020\sqrt2 e^{i\frac{3\pi}4+i2\pi n}) = \ln(2020\sqrt2)+(\frac{3\pi}4+2\pi n)i$$