# Math Help - complex numbers

1. ## complex numbers

given that z=5-7i and w=2<-pi/3

1)State Im(z)
2)arg(w)
3)Modulo of w

4)convert z to polar form and w to cartesain form

5) calculate z-w
zw
z/w

2. ## Re: complex numbers

What do you mean by 2 <- pi/3?

3. ## Re: complex numbers

its in polar form, 2<pi/3 is an complex number with an angle of pi/3 and length of 2

4. ## Re: complex numbers

Originally Posted by Magical
its in polar form, 2<pi/3 is an complex number with an angle of pi/3 and length of 2
Well then you need to write it as \displaystyle \begin{align*} 2\left(\cos{\frac{\pi}{3}} + i\sin{\frac{\pi}{3}}\right), 2\,\textrm{cis}\,\frac{\pi}{3} \end{align*} or \displaystyle \begin{align*} 2e^{i\frac{\pi}{3}} \end{align*}.

Anyway, what have you gotten so far?

5. ## Re: complex numbers

exactly what uve got 2(cospi/3 +isinpi/3)

6. ## Re: complex numbers

I mean, what have you tried for the answers to your questions?

7. ## Re: complex numbers

i get 7 for part 1, dont know how to do part 2 or 3

8. ## Re: complex numbers

7 is incorrect. It's actually -7.

As for part 2 and 3, the "modulus" of a complex number is its size or length. How long is \displaystyle \begin{align*} 2\left(\cos{\frac{\pi}{3}} + i\sin{\frac{\pi}{3}}\right) \end{align*}? The "argument" is the angle made. What is the angle in this complex number?

9. ## Re: complex numbers

the angle in the complex number is pi/3 and to find the length i would need to use root(a sqaured +b sqaures)

10. ## Re: complex numbers

Originally Posted by Magical
the angle in the complex number is pi/3 and to find the length i would need to use root(a sqaured +b sqaures)
You can. It's a bit pointless though. Any complex number in Polar form \displaystyle \begin{align*} r\left(\cos{\theta} + i\sin{\theta}\right) \end{align*} has a modulus of \displaystyle \begin{align*} r \end{align*}.