# Thread: solution to the equation (complex roots)

1. ## solution to the equation (complex roots)

I normally have no problem solving simple equations iand finding there complex roots but Could someone please help me solve this problem as the equation looks really nasty:

Thank you

Ps: I not sure if this problem is in the right section

2. Simply rearrange your equation to give

$\displaystyle z-\frac{i}{2} = (-i)^{\frac{1}{3}},$

then so long as you can find the third roots of $\displaystyle -i$ you can solve for $\displaystyle z.$

Write back if you need any help finding the third roots,

Cheers

3. Originally Posted by nimon
Simply rearrange your equation to give

$\displaystyle z-\frac{i}{2} = (-i)^{\frac{1}{3}},$

then so long as you can find the third roots of $\displaystyle -i$ you can solve for $\displaystyle z.$

Write back if you need any help finding the third roots,

Cheers
Thanks for the start i managed to do this but how would i got stuck after this.

4. The three cube roots of $\displaystyle -i$ are:
$\displaystyle \text{cis}\left(\frac{-\pi}{6}\right)~,~\text{cis}\left(\frac{\pi}{2}\rig ht)~\&~\text{cis}\left(\frac{-5\pi}{6}\right)$.

5. Thanks for the help, i can know finish the problem help off.