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Math Help - complex conjugate

  1. #1
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    complex conjugate

    can i ask if Z= r ( cos X + i sin X), then Z* = r ( cos X - i sin X) or Z* = (1/r) ( cos X - i sin X)

    thanks!
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  2. #2
    Junior Member utopiaNow's Avatar
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    Quote Originally Posted by alexandrabel90 View Post
    can i ask if Z= r ( cos X + i sin X), then Z* = r ( cos X - i sin X) or Z* = (1/r) ( cos X - i sin X)

    thanks!
    I'm assuming you're asking what the complex conjugate of z = r(\cos{X} + i\sin{X}) is? If, so then just remember if z = a + ib, where a, b \in \mathbb{R}, then the complex conjugate is simply \bar{z} = a - ib. So if we have z = r(\cos{X} + i\sin{X}), then if we re-arrange to get it to the form z = a + ib, we see we get z = r\cos{X} + ri\sin{X}. Therefore \bar{z} or z^* =  r\cos{X} - ri\sin{X} = r ( \cos{X} - i \sin{X}) is the complex conjugate.

    So to sum up complex conjugate of Z= r ( cos X + i sin X) is Z* = r ( cos X - i sin X).
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