Question

Simplify 13 over the quantity of negative 3 plus 2i.

Answer 1

$\frac{13}{(-3+2i)}$

To simplify we need to rationalize it. which can be done by multiplying composite of denominator. That is multiply by -3-2i

$=\frac{13}{(-3+2i)}*\frac{(-3-2i)}{(-3-2i)}$

Now multiply numerator with numerator and denominator with denominator

$=\frac{(-39-26i)}{(-3)^2-(-2i)^2}$

$=\frac{(-39-26i)}{9-(4i^2)}$

$=\frac{(-39-26i)}{9-(4(-1))}$

$=\frac{(-39-26i)}{9-(-4)}$

$=\frac{(-39-26i)}{9+4}$

$=\frac{(-39-26i)}{13}$

$=-3-2i$

Hence final answer is $=-3-2i$