Question 1116783: will you please heal me Find the cube roots of 8i. Write the answer in a + bi form? I honestly have no idea what I'm doing. I'm just trying to pass trigonometry to graduate.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! This is  , with  and  ,
plotted in the complex plane,
where you plot the real part of  , as  ,
and the imaginary part, as  :
The cube roots of 
are the three solutions to
     
With complex numbers written in the form ,
to multiply them, you multiply the  parts (called modulus or absolute value),
and you add the  angle part, (called argument).
As a consequence,
  .
So, what you have to solve is
 and  for  .
The result is  and  for .
So, the three values for are
 , with  and  ,
 , with  and  , and
 , with  and  ,
and the three cube roots of are
 ,
 , and
 .
They can be plotted, as three equally spaced points,
at distance  from the origin, like this:
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