Calculating Argument of w: (-4(√3+i))/(-1+i)

[SwedishFred]

Hi I am kind of lost
Deside an argument for w


w= (-4(√3+i))/(-1+i)

I know that the arg is the angel..
And the equation is in radians..

where to start??

best Regards!

Homework Equations

The Attempt at a Solution

 

[jbunniii]

Convert to polar coordinates?

 

[SwedishFred]

yeah i thought so to, but I am not really sure how..
z=r cos σ+i r sinσ=r(cos+i sin), i don't know how to use this ...

 

[jbunniii]

Hint: you should be able to convert these to polar coordinates easily:

$$\frac{\sqrt{3}}{2} + i \frac{1}{2}$$
and
$$-\frac{1}{\sqrt{2}} + i \frac{1}{\sqrt{2}}$$

 

[STEMucator]

Hint: Why don't you try multiplying the entire expression by: $\frac{- 1 - i}{- 1 - i}$.

Then switch to polar.

 

[SwedishFred]

i did try to multiply it, it gave me (3-√3+3i-√3i)/2 it looks wrong and it won't help me..
sorry Jbunniii i can´t .. thanks for your time..

 

[SwedishFred]

With little help from my friend i manage solve it, thanks guys..

 

[jbunniii]

Glad you were able to solve it. FYI, it's useful to remember the cosine and sine of three key angles: $\pi/6$, $\pi/4$, and $\pi/3$ (i.e., 30, 45, and 60 degrees). Then you can instantly recognize things like
$$\frac{\sqrt{3}}{2} + i \frac{1}{2} = \cos(\pi/6) + i \sin(\pi/6)$$