# solution to the equation (complex roots)

• Jan 16th 2010, 11:08 AM
SubZero
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:

Attachment 14856

Thank you

Ps: I not sure if this problem is in the right section
• Jan 16th 2010, 11:42 AM
nimon
Simply rearrange your equation to give

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

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

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

Cheers :)
• Jan 16th 2010, 12:03 PM
SubZero
Quote:

Originally Posted by nimon
Simply rearrange your equation to give

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

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

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.
• Jan 16th 2010, 12:28 PM
Plato
The three cube roots of $-i$ are:
$\text{cis}\left(\frac{-\pi}{6}\right)~,~\text{cis}\left(\frac{\pi}{2}\rig ht)~\&~\text{cis}\left(\frac{-5\pi}{6}\right)$.
• Jan 16th 2010, 12:37 PM
SubZero
Thanks for the help, i can know finish the problem help off.