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Homework Help: 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

    HallsofIvy

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    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

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    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!
     
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