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Math Help - Need help with trig (polar) for of a number...

  1. #1
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    Question Need help with trig (polar) for of a number...

    I am looking to find the trig/ polar form of 3 -the Sq root of 3i any help would be appreciated!
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by bemidjibasser View Post
    I am looking to find the trig/ polar form of 3 -the Sq root of 3i any help would be appreciated!
    So you are asked to convert z:= 3-\sqrt{3}i to the form |z|\cdot e^{i\phi}.

    You have |z|=\sqrt{3^2+\sqrt{3}^2}=\sqrt{12}=2\sqrt{3}, and \phi = \tan^{-1}\frac{-\sqrt{3}}{3}=-\frac{\pi}{6}.

    To sum up: 3-\sqrt{3}i=2\sqrt{3}\cdot e^{-i\frac{\pi}{6}}
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  3. #3
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    trig polar form

    is there a way to express that in another form? like with cosine and sin or not?
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  4. #4
    Super Member Failure's Avatar
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    Quote Originally Posted by bemidjibasser View Post
    is there a way to express that in another form? like with cosine and sin or not?
    Well, yes, you have that e^{i\varphi}=\cos(\varphi)+i\sin(\varphi).
    Given what I have already written above you this gives you

    3-\sqrt{3}i=2\sqrt{3}\cdot \big(\cos(-\pi/6)+i\sin(-\pi/6)\big).
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  5. #5
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    failure....

    Could you take a look at the polar form question I polsted above and offer some input as well? Thank you in advance.
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