Answer:
[tex]a + b = 9[/tex]
Step-by-step explanation:
We have a quadratic equation in z, given as:
[tex] {z}^{2} + az + b = 0[/tex]
with roots
[tex]z_1 = 2 + 3i \: and \: z_2 = 2 - 3i[/tex]
The sum of roots is given by:
[tex]z_1 + z_2 = - \frac{a}{1} [/tex]
This implies that
[tex]2 - 3i + 2 + 3i= - \frac{a}{1} [/tex]
[tex]4 = - a[/tex]
[tex]a = - 4[/tex]
Also product of roots is given by:
[tex]z_1z_2 = \frac{b}{1} [/tex]
This implies that:
[tex](2 + 3i)(2 - 3i) = b[/tex]
[tex]b = {2}^{2} + {3}^{2} [/tex]
[tex]b = 13[/tex]
Therefore
[tex]a + b = 13 - 4 = 9[/tex]
