[tex] \frac{13}{(-3+2i)} [/tex]
To simplify we need to rationalize it. which can be done by multiplying composite of denominator. That is multiply by -3-2i
[tex] =\frac{13}{(-3+2i)}*\frac{(-3-2i)}{(-3-2i)} [/tex]
Now multiply numerator with numerator and denominator with denominator
[tex] =\frac{(-39-26i)}{(-3)^2-(-2i)^2} [/tex]
[tex] =\frac{(-39-26i)}{9-(4i^2)} [/tex]
[tex] =\frac{(-39-26i)}{9-(4(-1))} [/tex]
[tex] =\frac{(-39-26i)}{9-(-4)} [/tex]
[tex] =\frac{(-39-26i)}{9+4} [/tex]
[tex] =\frac{(-39-26i)}{13} [/tex]
[tex] =-3-2i[/tex]
Hence final answer is [tex] =-3-2i[/tex]
