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.

Question 983323: What are the cube roots of ?
(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)   (Show Source): You can put this solution on YOUR website!

= 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 = ).

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

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.

RELATED QUESTIONS
What are the 5th roots of 1? (Answer using cis(x) where x is assumed to be in degrees.) (answered by ikleyn)

What are the 5th roots of 1? (Answer using cis(x) where x is assumed to be in degrees.) (answered by ikleyn)

Please help me solve this question in De Moivre's Theorem: What are the 4th roots... (answered by Alan3354)

Hi, My question is similar to 7723, but I'm not sure what to do with the square.... (answered by rapaljer)

Evaluate the following quotient: 1/√2+ 1/√2 *i/ 3*(√3/2-1/2i)... (answered by josgarithmetic)

Question: sqrt(x)-sqrt(3x-3)=1 My work: sqrt(x)-sqrt(3x-3)=1... (answered by math_tutor2020,ikleyn,MathTherapy)

{{{sqrt(3) cis 15}}} {{{2 cis 45}}} Multiply and express the answer in rectangular... (answered by Alan3354)

An expression is well-defined if you can compute its value without any illegal... (answered by ikleyn)

An expression is well-defined if you can compute its value without any illegal... (answered by Fombitz,ikleyn)