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Math Help - [SOLVED] Complex Numbers from Polar to Cartesian/Argand

  1. #1
    Junior Member Evales's Avatar
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    [SOLVED] Complex Numbers from Polar to Cartesian/Argand

    Hey,
    So basically I have been given a complex number and I have tried converting it but I am worried that I am doing it wrong. 3cis(pi/4)

    I was wondering if this complex number can come out exactly, and if there is a fast way of doing it/ checking it.

    Thanks
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  2. #2
    Super Member wingless's Avatar
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    3\cdot\text{cis}\frac{\pi}{4}

    3\cdot\text{cis}45

    3\cdot(\cos 45 + i \sin 45)

    You should know that \cos 45 = \sin 45 = \frac{\sqrt{2}}{2}.
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  3. #3
    Moo
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    Hello

    Quote Originally Posted by Evales View Post
    Hey,
    So basically I have been given a complex number and I have tried converting it but I am worried that I am doing it wrong. 3cis(pi/4)

    I was wondering if this complex number can come out exactly, and if there is a fast way of doing it/ checking it.

    Thanks
    cis(x)=e^{ix}=\cos x+i \sin x

    Therefore, 3 cis(\pi/4)=3e^{i \pi/4}=3(\cos \pi/4+i \sin \pi/4)

    Is it ok ?

    To check it...hm, I don't see any other way >.< maybe a graphical one, but it's more complicated in my opinion.
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