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Thread: Solve z^3 = 1 / i

  1. #1
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    Solve z^3 = 1 / i

    Hi, someone suggested online that this equation simplifies to z^3 + i = 0. Could I get an answer as to why? does z^3=1/i become z^3 = -i/1 ?? How can we do this? I don't recall any reciprocal rule being applied to an equation like that. Thanks
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  2. #2
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    Re: Solve z^3 = 1 / i

    z^3=1/i
    now in 1/i multiply numerator and denominator by i
    i^2=-1
    so -i=(1*i)/(i*i)
    so u get
    z^3=-i
    z^3+i=0
    Thanks from selsunblue
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  3. #3
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    Re: Solve z^3 = 1 / i

    Quote Originally Posted by selsunblue View Post
    Hi, someone suggested online that this equation simplifies to z^3 + i = 0. Could I get an answer as to why? does z^3=1/i become z^3 = -i/1 ?? How can we do this? I don't recall any reciprocal rule being applied to an equation like that. Thanks
    $\dfrac{1}{z} = \dfrac{{\overline z }}{{{{\left| z \right|}^2}}}$
    Thanks from selsunblue
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