Finding argument of complex number and conversion into polar form How do I find the argument of a complex number, for example $z = 3 + 4i$?
I know the polar form of $z$ is $r(\cos\theta + i\sin\theta)$ where $r$ is the modulus of $z$ ($\sqrt{3^2+4^2}$) which would leave me with $z = 5(\cos\theta+i\sin\theta)$, I'm just unsure how to deduce $\theta$ here.
The textbook says two things: $\theta = \arg(z)$ and $\tan\theta = b/a$, I'm not sure how these help.

Your textbook says that if you have $z = a+ bi$ then $\tan \theta = \frac{b}{a}$ so that $$\theta = \arctan \frac{b}{a}$$
In your case, this is $\theta = \arctan \frac{4}{3}$ for $z = 3+ 4i$. Although, really, the convention for the argument makes this not so straightforward. The Wikipedia article explains the computation of the argument well.
