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Complex numbers, find (3/(1-i)-(1-i)/2)^40?

  1. Oct 21, 2011 #1
    1. The problem statement, all variables and given/known data

    Please help me find (3/(1-i)-(1-i)/2)^40. I got a result (see below) but I'm not sure whether it is correct. Any help is appreciated. Thanks.

    2. Relevant equations

    3. The attempt at a solution

    I got (1+2i)^40. After this I got some funny numbers like 7^10*16*(6232-474*i).
  2. jcsd
  3. Oct 21, 2011 #2


    Staff: Mentor

    I get this (above) also.
    The way to go here is to convert 1 + 2i into polar form, using the Theorem of de Moivre. Then raising to the 40th power is easy.
    See http://en.wikipedia.org/wiki/De_Moivre's_formula.
  4. Oct 22, 2011 #3
    I know about de Moivre's formula. With it I get radius (r) to be sqrt(5) and angle 63.43 degrees. Again this is complicated to do by hand and I am wandering whether I got something wrong.
  5. Oct 22, 2011 #4


    User Avatar
    Homework Helper

    It is correct. But it might be that you or somebody else copied the problem wrong. (3/(1-i)-(1+i)/2)^40 would be easy.

  6. Oct 22, 2011 #5


    Staff: Mentor

    No, it's not complicated to do by hand once you have the complex number in this form.

    [r*e]n = rn*eniθ
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