Author Topic: Power of Complex Numbers with Arguments Hard to Determine Directly  (Read 323 times)

Yifei Hu

  • Newbie
  • *
  • Posts: 1
  • Karma: 0
    • View Profile
Question: let w= 2-i , find w^3 + w
Are we suppose to do multiplications directly or are we suppose to use Euler's formula? Since in this case, \theta = arctan(-1/2), we can't directly come out the sin and cos of n \theta.
Are there any other alternative methods to apply to such complex numbers with a general arguments that can take advantage of Euler's formula's easy computations of power? Can we give the answer to this question as a polynomial of e^iarctan(c)?

Victor Ivrii

  • Administrator
  • Elder Member
  • *****
  • Posts: 2563
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
Re: Power of Complex Numbers with Arguments Hard to Determine Directly
« Reply #1 on: September 24, 2020, 01:34:58 AM »
In this case usual cube of the sum would be the most efficient solution