# Complex No.s Question (arg)

• Apr 7th 2010, 02:42 AM
noobonastick
Complex No.s Question (arg)
Hey, can someone help with the following?

let z = (1+ sqrt(3)i ) and w = (1+i). Evaluate zw and hence show that cos (7*pi/12) = (1 - sqrt(3))/2*sqrt(2)

Thanks
• Apr 7th 2010, 02:53 AM
Bushy
By expanding first find $\displaystyle zw = (1+\sqrt{3}i)(1+i)$
• Apr 7th 2010, 03:24 AM
noobonastick
Quote:

Originally Posted by Bushy
By expanding first find $\displaystyle zw = (1+\sqrt{3}i)(1+i)$

oh i can do that with no problems. Its just the 2nd part I need help with.
• Apr 7th 2010, 03:30 AM
HallsofIvy
Quote:

Originally Posted by noobonastick
oh i can do that with no problems. Its just the 2nd part I need help with.

Good! What did you get? And do you know how to use "polar form" to multiply two complex numbers? The argument of that product is equal to the sum of the arguments of the two numbers. And, of course, $\displaystyle r cos(\theta)$ is the real part of the number with modulus r and argument $\displaystyle \theta$.
• Apr 7th 2010, 03:43 AM
noobonastick
Oh Thanks! I solved it.