How do you divide a complex number with an exponent term? Ok, so basically I have this:
$$ \frac{3+4i}{5e^{-3i}} $$
So basically, I converted the numerator into polar form and then converted it to exponent form using Euler's formula, but I can have two possible solutions.
I can have $5e^{0.972i}$ (radian) and $5e^{53.13i}$ (angle).
So my real question is, the exponent, does it have to be in radian or angle?
I ended up with $e^{3.927i}$.

A complex number $z=x+iy$ can be written as $z=re^{i\theta}$, where $r=|z|=\sqrt{x^2+y^2}$ is the absolute value of $z$ and $\theta=\arg{z}=\operatorname{atan2}(y,x)$ is the angle between the $x$-axis and $z$ measured counterclockwise and in radians. In this case, we have $r=5$ and $\theta=\arctan\frac{4}{3}$ (since $x>0$, see atan2 for more information), so $3+i4=5e^{i\arctan\frac{4}{3}}$ and
$$\frac{3+i4}{5e^{-i3}}=\frac{5e^{i\arctan\frac{4}{3}}}{5e^{-i3}}=e^{i(\arctan\frac{4}{3}+3)}\approx e^{i3.927}.$$
