Math - Complex Numbers

• Audi

  3 Apr 11, 12:57

  1. Express (3-i)^2 in the form a + ib.

  Hence or otherwise find the roots of the equation

  (z + i)^2 = -8 + 6i

  I am not sure how I can relate part one to part two. Need help over here.
  

   

  2.The complex numberx z and w have moduli k and 3k^2 respectively and arguments alfa and 4alfa respectively. where k is a positive constant and -pi/4 < alfa < pi/4. Express in the form a + ib.

  i) z^3

  ii) z/w*

  Basically I need help with part (ii). I manage to form the polar form of the expression but I got an angle of 5 alfa and I dont know how to find the basic angle.

  Thanks for helping.

• ThunderFbolt

  3 Apr 11, 15:12

  1. the answer for (3-i)^2 = 8 - 6i (done via (a+b)^2 = a^2 + 2ab + b^2)

  see the relation now?

   

   

• wee_ws

  3 Apr 11, 17:54

  Hi,

    For Q1, also consider the fact that i^2 = -1.

    Thanks.

  Cheers,
  Wen Shih

• wee_ws

  3 Apr 11, 18:20

  Hi,

    For Q2, we will start with -5pi/4 < 5 alpha < 5pi/4.

    Then we have to consider 3 cases:

    1. 5 alpha is within the principal range.

    2. 5 alpha is greater than pi.

    3. 5 alpha is less than -pi.

    Thanks.

  Cheers,
  Wen Shih