1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Complex number question

  1. Oct 30, 2005 #1
    This is a simple problem. Show that:
    (-1 + i)7 = -8(1 + i)
    where i = sqrt(-1)

    I'm able to prove this result by expanding the bracket:
    [(-1 + i)3]2(-1 + i)

    But please help me prove this using the polar form.
  2. jcsd
  3. Oct 30, 2005 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    Okay, PUT it in polar form! Polar form is [itex]r (cos(\theta)+ isin(\theta))[/itex] where r is the "magnitude" of the complex number (distance from 0) which is [itex]\sqrt{(-1)^2+ 1^2}= \sqrt{2}[/itex] for -1+ i and [itex]8\sqrt{2}[/itex] for -8(i+1). You can get [itex]\theta[/itex] by using [itex]\theta= arctan(\frac{Im}{Re})[/itex] but you should be able to see simply by plotting the points. -1+ i corresponds to (-1,1) in the plane so the angle is [itex]\frac{\3pi}{4}[/itex]. -(1+i)= -1-i corresponds to (-1, -1) so the angle is [itex]\frac{5\pi}{4}.[/itex].
    The seventh power of a complex number corresponds to taking the seventh power of r and multiplying [itex]\theta[/itex] by 7.
  4. Oct 30, 2005 #3

    Physics Monkey

    User Avatar
    Science Advisor
    Homework Helper

    Can you write z = -1 + i in polar form? What is the magnitude?

    I see Ivy has this handled.
  5. Nov 1, 2005 #4
    Thanks, HallsofIvy!! That was easy!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Complex number question
  1. Complex number question (Replies: 18)