SOLUTION: Find the sixth roots of -64. Enter the solutions in standard form, in any order. (Enter your answers separated by semicolons.) Thank you in advanced.

Question 984942: Find the sixth roots of -64. Enter the solutions in standard form, in any order.
(Enter your answers separated by semicolons.)
Thank you in advanced.
Answer by ikleyn(52795)   (Show Source): You can put this solution on YOUR website!
.
Notice that     -64 = 64(cos(180�) + i*sin(180�)).

The sixth roots of -64 are 6 complex numbers

1) 2(cos(30�) + i*sin(30�)) = = ;                                                 (Notice that 30� = 180�/6)

2) 2(cos(30�+60�) + i*sin(30�+60�)) = 2(cos(90�) + i*sin(90�)) = = ;       (Notice that 60� = 360�/6)

3) 2(cos(30�+120�) + i*sin(30�+120�)) = 2(cos(150�) + i*sin(150�)) = = ;

4) 2(cos(30�+180�) + i*sin(30�+180�)) = 2(cos(210�) + i*sin(210�)) = = ;

5) 2(cos(30�+240�) + i*sin(30�+240�)) = 2(cos(270�) + i*sin(270�)) = = ;

6) 2(cos(30�+300�) + i*sin(30�+300�)) = 2(cos(330�) + i*sin(330�)) = = .

If you want to see my lessons on complex numbers in this site, look in this
    - REVIEW of lessons on complex numbers
and especially in this one
    - How to take a root of a complex number.

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