SOLUTION: I'm 27 and not in school anymore. I didn't want you to think that I'm cheating on homework. I'm just trying to explain things better to my neice. I can't remember how to do complex

Question 137998: I'm 27 and not in school anymore. I didn't want you to think that I'm cheating on homework. I'm just trying to explain things better to my neice. I can't remember how to do complex cubes. This is the one I'm stuck on.
I need to find all three of the complex cube roots of 27 in the A+Bi form.
Found 2 solutions by scott8148, ptaylor:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
x^3=27 __ x^3-27=0

factoring difference of cubes __ (x-3)(x^2+3x+9)=0

using quadratic formula __ x=(-3 +- sqrt[(3^2-(4)(1)(9)])/[(2)(1)] __ x=[-3 +- sqrt(-27)]/2
__ x=-3/2 +- [(3/2)sqrt(3)]i

one root is real (3) __ roots are 3+0i, (-3/2)+[(3/2)sqrt(3)]i, (-3/2)-[(3/2)sqrt(3)]i
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
OK, Here's how you do it. Now we know, first of all, that all real numbers have one real root and two imaginary roots (Why? because inaginary roots occur in pairs)---27 is a real number
We also know, by inspection, that 3 is the real root of 27 because 3^3=27
If we let x^3=27, then x^3-27=0 This can be factored and we know what one factor is:
(x-3)(x^2 +?x+?)=0 In order to get the quadratic equation, we simply divide x-3 into x^3-27 and when we do that, we get x^2+3x+9. So now we have:
(x-3)(x^2+3x+9)=0
We'll solve x^2+3x+9 using the quadratic formula:

=
=
=

Check my math
Hope this helps---ptaylor

RELATED QUESTIONS
I might not have the topic exactly right, but I have an issue. This assignment was due... (answered by josgarithmetic,Edwin McCravy,MathLover1,ikleyn)
A problem on my math homework really gave me a hard time trying to understand it because... (answered by josgarithmetic,stanbon)
I think my problem with these kinds of questions is that I�m having a hard time... (answered by jsmallt9)
I just want to make sure that i have done this correctly. Simplify... (answered by stanbon,praseenakos@yahoo.com)
Which phrase does not have the same meaning as -3/w? (-3 is on top of the w like a... (answered by josgarithmetic,ikleyn,greenestamps)
Dear Tutor, Could you please explain the procedure in solving this problem: Let... (answered by Fombitz)
Q:The amount of barbeque sauce on VLC Spicy Wings is normally distributed with a mean of... (answered by ikleyn)
If a single letter is drawn from the set {m,a,t,h,e,i,c,s} what is the probability that... (answered by Fombitz)
Hi, I am trying to solve a problem-- I have to write a paragraph proof for If m<1=m<2,... (answered by midwood_trail)