SOLUTION: Hi There I'm really struggling with this question. How do i multiply the square root and fraction Find all possible roots of the complex number [27/2*(√3 +j)]^1/3 Than

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Hi There I'm really struggling with this question. How do i multiply the square root and fraction Find all possible roots of the complex number [27/2*(√3 +j)]^1/3 Than      Log On


   

Question 1136614: Hi There
I'm really struggling with this question. How do i multiply the square root and fraction
Find all possible roots of the complex number [27/2*(√3 +j)]^1/3
Thanks

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
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The number under the cubic root is  %2827%2F2%29%2A%28sqrt%283%29+%2B+j%29.


Present it in the trigonometric form.


The modulus is  %2827%2F2%29%2Asqrt%28%28sqrt%283%29%29%5E2+%2B+1%5E2%29%29 = %2827%2F2%29%2Asqrt%284%29 = 27.


The argument is  arctan%281%2Fsqrt%283%29%29 = 30°.


Now apply the de Moivre's formula.


The third degree roots of your number are 


    1)  3*cis(10°) = 3%2A%28cos%2810%5Eo%29+%2B+j%2Asin%2810%5Eo%29%29;


    2)  3*cis(130°) = 3%2A%28cos%28130%5Eo%29+%2B+j%2Asin%28130%5Eo%29%29;


    3)  3*cis(250°) = 3%2A%28cos%28250%5Eo%29+%2B+j%2Asin%28250%5Eo%29%29.

Solved.