Image sets in Complex Analysis I was given the problem "what is the image set of the first quadrant in the $z$ plane under the mapping $w=z^4$, but I have no idea how to even think about this.
The most I did was write $w=|z|^4 (\cos(4\theta) +i\sin(4\theta))$
But again, Im not sure if that's helpful or not. How do we picture things like this?

HINT
The complex number $(r, \theta)$ is mapped to $\left(r^4, 4 \theta\right)$.
What is the range of $r$ and $\theta$? What is the range of $r^4$ and $4 \theta$? What is the resulting range for $\left(r^4, 4 \theta\right)$?
