Complex Numbers ( Roots)
Find the three cubic roots of -1
a> cos π/3 + i sin π/3, cos 3π + i sin 3π , cos 2π/3 + i sin 2π/3
b> cos π/3 + i sin π/3, cos π + i sin π, cos 5π/3 + i sin 5π/3
c> cos π/2 + i sin π/2, cos π + i sin π, cos 5π/2 + i sin 5π/2
d> cos π/4 + i sin π/4, cos π + i sin π, cos 5π/4 + i sin 5π/4
Any help would be greatly appreciated
please show step by step!
Originally Posted by Daniels4691
write -1 in exponential
n take the values (1,2,3) since you want the cube square
take the cube square for the both sides ......... the rest for you
If , then the nth roots of a complex number would be in the form of
where k = 0, 1, 2, ... n - 1.
In our case, n = 3, r = 1, and k will go from 0 to 2. The angle simplifies to
The three cube roots of are:
... or answer choice (B).