Question

I need help urgently!!

Find zw and z/w. Leave your answers in polar form.

z=5-5i
w=sqrt(3)+i

Answer 1

Do you know what the polar form of z is?

Answer 2

No.

Answer 3

ok, so do you know what polar form looks like?

Answer 4

Yes, (r,theta).

Answer 5

ok, so in polar in terms of complex numbers means it looks like this :\[re^{i\theta}=r(cos\theta+isin\theta)\]

Answer 6

Okay. How do we begin converting it? Because, I don't understand that part, I mean. \[(5-5i)/(\sqrt{3}+i)\]

Answer 7

If \[
z=x+yi
\]Then... \[
r=\sqrt{x^2+y^2}\\
\theta = \tan^{-1}\left(\frac yx\right)
\]

Answer 8

It's the same \((x,y)\to (r,\theta)\) you learn in Calc

Answer 9

thank wio... I was just getting to that point

Answer 10

which is why I think complex analysis is so much bs.

Answer 11

So, if you would graph your point in the complex plane, it would look like this:

Answer 12

\[r=7.07, \Theta=\frac{ -5 }{ 5 }\]

Is that correct?

Answer 13

so then you need to find your r, thhis is how we derive it all

Answer 14

so can you find the hypotenuse of the triangle I've drawn?

Answer 15

Yes, I already did. Sqrt{50}

Answer 16

yes, ok so now, what is the exact value of theta?

Answer 17

-5/5