Complex numbers (modulus and argument)

Question

Find the modulus and argument of $ (4+2i)(-3+√2i)$ My attempt at Solution:

Expanding, we get $-12+4√2i+6i+2i√2i= -12+6i+4√2i+2i√2i$

I'm stuck here

Answer 1

$4+2i=\sqrt{20}e^{i\tan^{-1}(1/2)},-3+\sqrt2i=\sqrt{11}e^{i\tan^{-1}(-\sqrt2/3)}$

$\therefore r=\sqrt{220},\theta=\tan^{-1}(1/2)+\tan^{-1}(-\sqrt 2/3)$.