# How do you write a polynomial equation of least degree given the roots 6, 2i, -2i, i, -i?

Apr 23, 2017

${z}^{5} - 6 {z}^{4} + 5 {z}^{3} - 30 {z}^{2} + 4 z - 24 = 0$

#### Explanation:

$\left(z - 6\right) \left(z - 2 i\right) \left(z - \left(- 2 i\right)\right) \left(z - i\right) \left(z - \left(- i\right)\right) = 0$
$\left(z - 6\right) \left(z - 2 i\right) \left(z + 2 i\right) \left(z - i\right) \left(z + i\right) = 0$
$\left(z - 6\right) \left({z}^{2} - 2 z i + 2 z i - 4 {i}^{2}\right) \left({z}^{2} - z i + z i - {i}^{2}\right) = 0$
$\left(z - 6\right) \left({z}^{2} + 4\right) \left({z}^{2} + 1\right) = 0$
$\left(z - 6\right) \left({z}^{4} + 4 {z}^{2} + {z}^{2} + 4\right) = 0$
$\left(z - 6\right) \left({z}^{4} + 5 {z}^{2} + 4\right) = 0$
${z}^{5} - 6 {z}^{4} + 5 {z}^{3} - 30 {z}^{2} + 4 z - 24 = 0$