How do I use a graphing calculator to find the complex zeros of x^3-1?

Sep 23, 2015

Explanation:

Using the difference formula for perfect cubes :

${x}^{3} - 1 = \left(x - 1\right) \left({x}^{2} + x + 1\right)$

So, this cubic has one real zero at x = 1. The other two roots are imaginary. You can use the quadratic formula to solve for these other two roots:

$x = \frac{- 1 \pm \sqrt{1 - \left(4\right) \left(1\right) \left(1\right)}}{\left(2\right) \left(1\right)}$

$x = - 0.5 \pm 0.5 i \sqrt{3}$

Hope that helped!