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Thread: complex numbers query

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    complex numbers query

    heey so suppose I have 5-5i = 5 root 2 (cosx+isinx)

    now i have to equate the roots to eventually get x
    is it always the case that I can choose to equate the real or imaginary and it doesn't matter which one? do I always get the same answer??

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    Junior Member 1729's Avatar
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    Re: complex numbers query

    Quote Originally Posted by sssona09 View Post
    heey so suppose I have 5-5i = 5 root 2 (cosx+isinx)

    now i have to equate the roots to eventually get x
    is it always the case that I can choose to equate the real or imaginary and it doesn't matter which one? do I always get the same answer??

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    Junior Member 1729's Avatar
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    Re: complex numbers query

    Quote Originally Posted by sssona09 View Post
    heey so suppose I have 5-5i = 5 root 2 (cosx+isinx)

    now i have to equate the roots to eventually get x
    is it always the case that I can choose to equate the real or imaginary and it doesn't matter which one? do I always get the same answer??

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    Re: complex numbers query

    Quote Originally Posted by 1729 View Post
    how do we know that? by plotting?

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    Member jathu123's Avatar
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    Re: complex numbers query

    for complex number z=a+ib, arg(z) = arctan(b/a) [-pi < arg(z) ≤ pi]
    and its clear that 5-5i is in the 4th quadrant, so the argument of 5-5i is arctan(-1) = -pi/4
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    Re: complex numbers query

    Quote Originally Posted by 1729 View Post
    thank you so much for helping it makes sense now

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    Re: complex numbers query

    Quote Originally Posted by jathu123 View Post
    for complex number z=a+ib, arg(z) = arctan(b/a) [-pi < arg(z) ≤ pi]
    so the argument of 5-5i is arctan(-1) = -pi/4
    ohhhh thanksss

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    Re: complex numbers query

    Quote Originally Posted by 1729 View Post
    Hey what if the domain is x between 0 and pi/2
    would i say that sinx has no solutions?? both should hold true so..

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