Question

which expression is a cube root of -2?
A.)^3sqrt2(cos120)+isin(120))
b.) ^3sqrt2(cos60)+isin(60))
c.) ^3sqrt2(cos260)+isin(260))
d^3sqrt2(cos(90)+isin(90))

Answer 1

Do you know de Moirvre's theorem?

Answer 2

no :(

Answer 3

how about the roots of unity?

Answer 4

not really

Answer 5

Have you done any one of the above in school? If not, the question is not for you! lol

Answer 6

the question is on a guide for next years math class. i just want to understand it

Answer 7

Ok, that explains it.
I suggest you first do some reading on de Moivre's theorem, which will be used to get the roots of unit. They are both very interesting topics. Have you done anything with complex numbers?

Answer 8

some things but not alot

Answer 9

Good, here's an example of the complex plane.
The vertical axis represents the value of i, I call it the imaginary axis.
The horizontal axis is the real axis, that we generally work with every day.
The circle has a radius of one (unity).
So to the right of the origin, the point is (1,0i), or simply (1,0)
The point above the origin has coordinates (0,1), or (0,i), etc.

The four points divide 2pi equally, namely 360/4 = 90 degrees apart. The interesting part is that each of the four points is a fourth root of 1, i.e.
(1+0i)^4=1
(0+i)^4=1
(-1+0i)^4=1
(0-i)^4=1
So these are the four fourth roots of unity.
You can use the example to figure out the problem you posed.
If you have problems, do some reading, such as:
https://www.artofproblemsolving.com/wiki/index.php?title=Roots_of_unity
or google "roots of unity" to choose from videos or articles.