Question
Find the 5 roots of x^5+1=0 in polar and Cartesian form. (x^5 means x to the 5th power)
x^5 = -1 = e^[i (2n + 1) pi]
where i is any integer
x = [e^[i (2n + 1) pi]]^(1/5)
= e^(i pi/5)= cos pi/5 + i sin (pi/5)
= e^(3 i pi/5)
= cos (2 pi/5) + i sin (2 pi/5)
etc.
x^5 = -1 = e^[i (2n + 1) pi]
where i is any integer
x = [e^[i (2n + 1) pi]]^(1/5)
= e^(i pi/5)= cos pi/5 + i sin (pi/5)
= e^(3 i pi/5)
= cos (2 pi/5) + i sin (2 pi/5)
etc.