I have a following equation
$$ |B| = \sqrt{\frac{2}{L}}, $$
$B$ being a complex number and $L$ being a real one.
The solution is supposed to be $$ B = \sqrt{\frac{2}{L}}e^{i\alpha}, $$
$\alpha$ being an arbitrary real number.
I can imagine the values being on a circle, all in the same distance from the point $B$, but I'm not able to derive the above-mentioned result mathematically, since it's been a pretty long time from my last complex analysis course.
I know, that: \begin{align} B &= x + iy\\ |B| &= \sqrt{x^2 + y^2}\\ \sqrt{x^2 + y^2} &= \sqrt{\frac{2}{L}}\\ x^2 + y^2 &= \frac{2}{L}, \end{align}
but this is obviously not the correct solution and I don't see the way to achieve the correct one step-by-step.
Could you help me?