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Thread: Complex number arguments

  1. #1
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    Complex number arguments

    Hi I don't understand how the answer to this question came about.

    Find the argument expressed in the range of (-pi , pi] of -3ie-(iπ/4)

    Thank you! Why is it not -pi/4?
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  2. #2
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    Re: Complex number arguments

    Because -3i=3e^{i\pi}e^{i\frac{\pi}{2}}
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  3. #3
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    Re: Complex number arguments

    Quote Originally Posted by princessp View Post
    Hi I don't understand how the answer to this question came about.

    Find the argument expressed in the range of (-pi , pi] of -3ie-(iπ/4)

    Thank you! Why is it not -pi/4?
    I think that you are correct. See HERE.
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  4. #4
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    Re: Complex number arguments

    You've entered the wrong expression into Wolfram Alpha. Rubbish in -> rubbish out.
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  5. #5
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    Re: Complex number arguments

    Quote Originally Posted by Archie View Post
    Because -3i=3e^{i\pi}e^{i\frac{\pi}{2}}
    just to finish this (because it was confusing me)

    $-3i = 3e^{i \pi}e^{i \pi/2} = 3e^{3\pi/2} \to 3 e^{-\pi/2}$

    because $\dfrac {3\pi}{2} > \pi$

    now

    $3 e^{-\pi/2}e^{-\pi/4} = 3 e^{-3\pi/4}$

    $Arg\left( 3 e^{-3\pi/4}\right) = -\dfrac {3\pi}{4}$
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  6. #6
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    Re: Complex number arguments

    Quote Originally Posted by princessp View Post
    Hi I don't understand how the answer to this question came about.

    Find the argument expressed in the range of (-pi , pi] of -3ie-(iπ/4)
    Thank you! Why is it not -pi/4?
    The correct answer is $\large\dfrac{-3\pi}{4}$ See HERE.

    $\large\text{Arg}(-3\bf{i})=\dfrac{-\pi}{2}$ and $\large\text{Arg}\left(\exp(-\frac{\bf{i}\pi}{4}\right)=\dfrac{-\pi}{4}$ the sum of which is $\large\dfrac{-3\pi}{4}$
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