2
$\begingroup$

Could someone please help me write $z = \dfrac{(2+2i)^3}{(1+i\sqrt{3})^4}$ on polar form?

$|z|=\sqrt{2}$

But how do I proceed to get the argument?

$\mathrm{arg⁡}(z)=\mathrm{arg⁡}(2+2i)^3 - \mathrm{arg⁡}(1+i\sqrt{3})^4$

Thanks /David

  • 2
    Welcome to math.stackexchange! Why don't you break this problem into smaller pieces first: Find the polar forms of $2+2i$ and $1+i\sqrt{3}$ first. Then can you find the full answer?2011-11-04
  • 1
    For integer $n,\arg(z^n)=n\arg(z)$, which you can see from writing $z=r\exp(i\theta)$2011-11-04
  • 0
    @David: Another hint: Let $z_1= |z_1|exp(i \alpha)$ and $z_2= |z_2|exp(i \beta)$. Then $z_1/z_2= (|z_1|/|z_2|)exp (i (\alpha - \beta))$.2011-11-04

3 Answers 3