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Math Help - Cubed roots of complex numbers in polar form

  1. #1
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    Cubed roots of complex numbers in polar form

    I am taking a power series and matrices class and as part of the review we are being asked to determine the possible polar angles if we have the cube roots of 1 + i

    I am at a complete loss as to how to tackle this. Would I just use r = the square root of (1^1/3 + 1^1/3) since the coefficient for i is one

    and then use polar form: z = r cos angle + i r sin angle?????

    Thanks to all of you who take time to help out struggling math students!!! Frostking
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  2. #2
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    Quote Originally Posted by Frostking View Post
    I am taking a power series and matrices class and as part of the review we are being asked to determine the possible polar angles if we have the cube roots of 1 + i

    I am at a complete loss as to how to tackle this. Would I just use r = the square root of (1^1/3 + 1^1/3) since the coefficient for i is one

    and then use polar form: z = r cos angle + i r sin angle?????

    Thanks to all of you who take time to help out struggling math students!!! Frostking
    1 + i = \sqrt{2} \text{cis} \left( \frac{\pi}{4} + 2n\pi\right). Take the cube root and then substitute n = 0, 1 and 2 to get the arguments.
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  3. #3
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    Just to clarify, "cis(x)" is "engineering speak" for cos(x)+ i sin(x).
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  4. #4
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    Quote Originally Posted by HallsofIvy View Post
    Just to clarify, "cis(x)" is "engineering speak" for cos(x)+ i sin(x).
    Which is fascinating since engineers use j to represent \sqrt{-1} (i could get confused with the symbol for current. And it may surprise some viewers that there is a very strong link between electrical circuit theory and complex numbers).
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