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

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- Apr 7th 2010, 02:42 AMnoobonastickComplex 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 AMBushy
By expanding first find $\displaystyle zw = (1+\sqrt{3}i)(1+i)$

- Apr 7th 2010, 03:24 AMnoobonastick
- Apr 7th 2010, 03:30 AMHallsofIvy
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 AMnoobonastick
Oh Thanks! I solved it.