Complex numbers

• Audi

  17 Apr 11, 22:00

  Alright this is urgent. Been trying to solve this for some time but couldnt. Please do show the any step by step method to solving this.

  Write down the roots for the equation z^3 = 1 in the form re^i(theta) -> euler form

  Find in euler form all the complex numbers z such that z^3 = (5+i)/(2+3i)

  Find the exact values of w such that ((1+iw)/(1-iw))^3 = 1, giving your answer in the form a + ib.

  Need help in the highlighted, bold part. Will appreciate any help i can get by monday morning! Thank you.

• wee_ws

  18 Apr 11, 08:23

  Hi,

    1. (1 + iw) / (1 - iw) = 1, e^i(2pi/3) or e^i(-2pi/3).

    2. Express each root in cartesian form.

    3. For each root, make w the subject.

    Thanks.

  Cheers,
  Wen Shih