# Finding the abs. value and argument of a complex number?

Given the following complex number:

I'm asked to find the abs. value and the argument, I found both in rectangular form, is that considered incorrect? Or must I convert it to polar form then solve $|z|$ and $\theta$?

I solved each individual complex number,simplified, used the conjugate, and then used the formula $|z| = \sqrt{ x^2 + y^2}$, and $\theta = \tan^{-1} (\frac{y}{x}$)

Or must I convert to polar form and solve the problem?

• Certainly, the easiest way to do this is to use polar coordinates. One could of course do it without using them, but it's hard to see the point for that. – Scounged Mar 9 '16 at 12:15
• @Scounged I agree, I took the longer method of solving it without using polar form, but since our instructor didn't specify which form, I think it's okay. Sadly though, I wasted 20mins instead of 5mins, but it taught me how both are the same(assuming the arithmetic is correct). – Pupil Mar 9 '16 at 12:33