# Question #00dfc

Oct 17, 2017

The first three output values are $\left(- 2 + 2 i\right)$, $\left(- 3 + 6 i\right)$, and $\left(- 30 + 38 i\right)$

#### Explanation:

${i}^{2} = - 1$

Use $z = 1$ as the first input value

$F \left(z\right) = {z}^{2} - 3 + 2 i$

$F \left(1\right) = 1 - 3 + 2 i = - 2 + 2 i$

Then $z = - 2 + 2 i$

$F \left(- 2 + 2 i\right) = {\left(- 2 + 2 i\right)}^{2} - 3 + 2 i = {\left(2 - 2 i\right)}^{2} - 3 + 2 i$

$= 4 - 8 i + 4 {i}^{2} - 3 + 2 i$

$= 4 - 8 i - 4 - 3 + 2 i$

$= - 3 - 6 i$

And finally $z = - 3 - 6 i$

$F \left(- 3 - 6 i\right) = {\left(- 3 - 6 i\right)}^{2} - 3 + 2 i$

$= 9 + 36 {i}^{2} + 36 i - 3 + 2 i$

$= - 30 + 38 i$