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Math Help - Question involving complex numbers

  1. #1
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    Question involving complex numbers

    Hi I really do not know how to do this.

    Write sin2a-cos2ai in modulus argument form
    I was thinking of changing sin2a to cos(pi/2 - 2a)..

    Will really appreciate the help! Thanks,
    J.
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  2. #2
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    Re: Question involving complex numbers

    Hey Tutu.

    What is modulus argument form? Is that in terms of re^(i*theta) where r = 1?
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    Re: Question involving complex numbers

    Quote Originally Posted by Tutu View Post
    Hi I really do not know how to do this.

    Write sin2a-cos2ai in modulus argument form
    I was thinking of changing sin2a to cos(pi/2 - 2a)..

    Will really appreciate the help! Thanks,
    J.
    Notice this is in the Cartesian Form \displaystyle \begin{align*} x + y\,i \end{align*} with \displaystyle \begin{align*} x = \sin{(2a)} \end{align*} and \displaystyle \begin{align*} y = \cos{(2a)} \end{align*}. You need to write it in the modulus-argument form \displaystyle \begin{align*} r\, e^{i\,\theta}  \end{align*} with \displaystyle \begin{align*} r = \sqrt{x^2 + y^2} \end{align*} and \displaystyle \begin{align*} \theta = \arctan{\left( \frac{y}{x} \right)} \end{align*}.
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  4. #4
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    Re: Question involving complex numbers

    From what I've learnt, modulus-argument form is the polar form where it is rcis(thetha) where r is positive.
    re^i(thetha) is exponential form for me.

    The answer of this question is in cis form, not exponential form.
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  5. #5
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    Re: Question involving complex numbers

    Quote Originally Posted by Tutu View Post
    From what I've learnt, modulus-argument form is the polar form where it is rcis(thetha) where r is positive.
    re^i(thetha) is exponential form for me.

    The answer of this question is in cis form, not exponential form.
    The calculation of \displaystyle \begin{align*} r \end{align*} and \displaystyle \begin{align*} \theta \end{align*} is identical.
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  6. #6
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    Re: Question involving complex numbers

    Sorry, I do not understand..
    Can you show me how you would do it?
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    Re: Question involving complex numbers

    You already have x and y. Evaluate \displaystyle \begin{align*} r = \sqrt{x^2 + y^2} \end{align*} and \displaystyle \begin{align*} \theta = \arctan{\left( \frac{y}{x} \right)} \end{align*}.
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