SOLUTION: What are the cube roots of {{{(1/2-(sqrt(3)/2) *i)}}}? (Answer using cis(x) notation where x is assumed to be in degrees.) Do not include the degree symbol in your answers.

Algebra ->  Trigonometry-basics -> SOLUTION: What are the cube roots of {{{(1/2-(sqrt(3)/2) *i)}}}? (Answer using cis(x) notation where x is assumed to be in degrees.) Do not include the degree symbol in your answers.       Log On


   

Question 983323: What are the cube roots of %281%2F2-%28sqrt%283%29%2F2%29+%2Ai%29?
(Answer using cis(x) notation where x is assumed to be in degrees.)
Do not include the degree symbol in your answers.
P.S. In the original problem to sqrt(3)/2 does not have a parentheses around it.
Thank you in advanced.
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!

1%2F2-%28sqrt%283%29%2F2%29%2Ai = cos(-60) + i*sin(-60) = cos(300) + i*sin(300)       (the angles are in degrees).

Three complex cubic roots of this number are

1.  cos(100) + i*sin(100)       (100 = 300%2F3).

2.  cos(100+120) + i*sin(100+120) = cos(220) + i*sin(220)       (120 = 360%2F3)

3.  cos(100 + 240) + i*sin(100+240) = cos(340) + i*sin(340)

See my lessons on complex numbers in this site  REVIEW of lessons on complex numbers  and especially the lesson  How to take a root of a complex number.