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Complex Numbers

  1. Mar 30, 2004 #1
    I have to find the principal root of [tex]\sqrt[3]{8 i}[/tex]
    But I get stuck at this part
    change this to polar coordinates...
    [tex]r= \sqrt {x^2 + y^2} [/tex]
    which makes [tex]r=8[/tex]
    but when I try to find [tex]\theta[/tex]
    [tex]\theta = \arctan \frac{y}{x}[/tex]
    from the original x = 0 so how do I find [tex]\theta[/tex]?
  2. jcsd
  3. Mar 30, 2004 #2


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    Science Advisor

    Don't just use formulas without thinking! When you say change "this" to polar coordinates you mean 8i: in the complex plane, that's the point (0, 8)- on the positive imaginary (y) axis which makes a right angle with the real (x) axis- [itex]\theta[/itex] is [itex]\frac{\pi}{2}[/itex] or 90 degrees.

    (Of course, [itex]\theta= arctan\frac{y}{x}[/itex] does work even in this case: [itex]tan(\frac{\pi}{2}) [/itex] is undefined.}
  4. Mar 31, 2004 #3
    Thanks for your help, I found the answer :smile:
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