# Thread: Solve z^3 = 1 / i

1. ## 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

2. ## 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

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

Originally Posted by selsunblue
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
$\dfrac{1}{z} = \dfrac{{\overline z }}{{{{\left| z \right|}^2}}}$