Originally Posted by

**Plato** .

I have told you this before, here it is again. For the life of me, I cannot understand what sort of course you are doing in which you are asked questions having been given not reals tools to use.

**For any complex number** $\displaystyle z = a + bi$ to give the polar form it is necessary to find the argument.

That is associated with the tangent function.

If $\displaystyle a=0$ then the argument is $\displaystyle \pm\dfrac{\pi}{2}$.

If $\displaystyle a\ne 0$ then the quantity $\displaystyle \left| {\ffrac{b}{a}} \right|$ is the tangent of the argument given the correct sign.

To find the correct sine, you need to see where the number is located on the graph.

YOU need to know the tangents of each of the following:

$\displaystyle 0,~\dfrac{\pi}{2}.~\pi,~\dfrac{3\pi}{2}~\dfrac{\pi }{6}~\dfrac{\pi}{3}~\dfrac{2\pi}{3}~\dfrac{5\pi}{6 }~\dfrac{7\pi}{6}$ etc.