Let's review polar form quick:

Recall $r\mbox{cis}(\theta) = r\cos(\theta) + i\cdot r\sin(\theta)$. What is the modulus of this? It is$$\sqrt{r^2\cos^2(\theta) + r^2\sin^2(\theta)} = \sqrt{r^2} = r.$$Hence if $r\neq 1$, then the modulus of $r^n$ is not $1$ so it can't equal to $1$. This is the main idea why $r=1$ for the roots of unity.

In general this is one of the main advantages of polar form. If we write a complex number as $r\mbox{cis}(\theta)$ then the $r$ (the modulus) and the $\theta$ (the argument) are somewhat independent from each other. The modulus tells us how far away the number is from the origin and the argument gives the angle.

Hence, if we have two complex numbers $r\mbox{cis}(\theta)$ and $s\mbox{cis}(\phi)$, as long as $r$ and $s$ are positive, then the two complex numbers are equal if and only if $r = s$ and $\phi = \theta \pm 2\pi\cdot k$ for some integer $k$. (The angle isn't unique because sine and cosine have period $2\pi$.)

Note: I highly recommend trying to think of the complex numbers visually, drawing out some examples and pictures as needed. Let us know if you have additional questions.