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Math Help - Polar Form

  1. #1
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    Polar Form

    Hey guys wondered if someone could help me out again, if you let Z=root 3 - i what is Z in polar form?

    Then how do I find the real and imaginary parts of (z^7)/8?
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  2. #2
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    Quote Originally Posted by Mathsnewbie View Post
    Hey guys wondered if someone could help me out again, if you let Z=root 3 - i what is Z in polar form?

    Then how do I find the real and imaginary parts of (z^7)/8?
    x= r cos(\theta) and y= r sin(\theta) so [tex]x^2+ y^2= r^2 cos^2(\theta)+ r^2 sin^2(\theta)= r^2[/itex]: r= \sqrt{x^2+ y^2}. Dividing y by x, y/x= sin(\theta)/cos(\theta)= tan(\theta) and [tex]\theta= arctan(y/x)[/itex].
    Here, x^2+ y^2= 3+ 1= 4 so r= 2. [tex]y/x= -1/\sqrt{3}[tex] so [tex]tan(\theta)= -1/\sqrt{3}[/itex] and \theta= -\pi/6.

    Once you have Z in polar form, Z^8 has r= 2^8= 256 and [tex]\theta= 8(-\pi/6)= -4\pi/3[/itex]. The real part of Z^8 is 256 cos(4\pi/3) and the imaginary part is - 256 sin(4\pi/3).
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