# How do you find all the real and complex roots of #z^3 +1 = 0#?

##### 1 Answer

Jan 15, 2016

Factor then solve the remaining quadratic using the quadratic formula to find:

#z = -1# or#z = 1/2+-sqrt(3)/2i#

#### Explanation:

#0 = z^3+1 = (z+1)(z^2-z+1)#

Solve

#z = (-b+-sqrt(b^2-4ac))/(2a) = (1+-sqrt(-3))/2 = 1/2+-sqrt(3)/2i#

Hence