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Math Help - How do you find the conjugate of -2/i^3?

  1. #1
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    How do you find the conjugate of -2/i^3?

    What is the conjugate of \frac{\ -2}{i^3}?
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    Re: How do you find the conjugate of -2/i^3?

    \frac{-2}{i^3}=\frac{-2i}{i^4}=-2i.
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    Re: How do you find the conjugate of -2/i^3?

    To find the conjugate of any complex number, replace i with -i. You could "rationalize the denominator" first, as "a tutor" did:
    \frac{-2}{i^3}= -2i and then its conjugate is -2(-i)= 2i. Or you can immediately write that the conjugate is \frac{-2}{(-i)^3}= \frac{2}{i^3}. If you were then to multiply both numerator and denominator by i you would again get \frac{2i}{i^4}= \frac{2i}{(i^2)^2}= \frac{2i}{(-1)^2}= 2i.
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    Re: How do you find the conjugate of -2/i^3?

    aw...i was gonna say find its minimal real polynomial, and grab the other root :P
    Last edited by Deveno; August 15th 2012 at 05:55 PM.
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    Re: How do you find the conjugate of -2/i^3?

    What's the reason you multiplied the numerator and denominator by i?
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    Re: How do you find the conjugate of -2/i^3?

    Quote Originally Posted by viccal View Post
    What's the reason you multiplied the numerator and denominator by i?
    tutor used the fact that i^4 = 1 in order to get \frac{-2}{i^3} in the form a \pm bi in an efficient manner.

    he ended up with -2i = 0 - 2i ... note that the conjugate is 0 + 2i = 2i
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