# Thread: Need help with trig (polar) for of a number...

1. ## Need help with trig (polar) for of a number...

I am looking to find the trig/ polar form of 3 -the Sq root of 3i any help would be appreciated!

2. Originally Posted by bemidjibasser
I am looking to find the trig/ polar form of 3 -the Sq root of 3i any help would be appreciated!
So you are asked to convert $\displaystyle z:= 3-\sqrt{3}i$ to the form $\displaystyle |z|\cdot e^{i\phi}$.

You have $\displaystyle |z|=\sqrt{3^2+\sqrt{3}^2}=\sqrt{12}=2\sqrt{3}$, and $\displaystyle \phi = \tan^{-1}\frac{-\sqrt{3}}{3}=-\frac{\pi}{6}$.

To sum up: $\displaystyle 3-\sqrt{3}i=2\sqrt{3}\cdot e^{-i\frac{\pi}{6}}$

3. ## trig polar form

is there a way to express that in another form? like with cosine and sin or not?

4. Originally Posted by bemidjibasser
is there a way to express that in another form? like with cosine and sin or not?
Well, yes, you have that $\displaystyle e^{i\varphi}=\cos(\varphi)+i\sin(\varphi)$.
Given what I have already written above you this gives you

$\displaystyle 3-\sqrt{3}i=2\sqrt{3}\cdot \big(\cos(-\pi/6)+i\sin(-\pi/6)\big)$.

5. ## failure....

Could you take a look at the polar form question I polsted above and offer some input as well? Thank you in advance.