cube roots of -1 lies in the region given in the best options are A. on real axis, B. quadrant 1, F. quadrant 4.
<h3>What is cube roots of -1?</h3>
Cube roots of -1 mean "finding solution of the equation z³ = -1 since the equation is of order 3, the equation has 3 roots in complex field."
According to the question,
Cube roots of -1 can written as
First, write the given number in polar form
Add 2kπ to the argument
Apply De Moivre's theorem
x =
Put k = 0,1,2..., (n-1) [sin (-θ) = -sin θ, cos(-θ) = cos θ]
The three roots are
cos 0 - sin 0, cos , , cos , sin
-1, , are the three roots of cube roots of -1
It can be seen that the three roots lies in the regions of real axis, quadrant 1 and quadrant 4.
Hence, cube roots of -1 lies in the region given in the best options are A. on real axis, B. quadrant 1, F. quadrant 4.
Learn more about cube roots here:
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