Question

Can anyone help me with number 36? I’m trying to figure out how to do this am I’m having a lot of problems. The answer is in the box, I just don’t know how to get there. Thank you so much

Answer 1

You have 9i in the denominator. The goal is to have a real denominator. 9i is imaginary. i * i = -1 which is real. If you multiply the denominator by i, the denominator will be real. Since this is a fraction, we multiply the numerator and denominator by i.

$\dfrac{-6 - 10i} {9i } \times \dfrac{i}{i} =$

$= \dfrac{(-6 - 10i)i}{(9i)i}$

$= \dfrac{-6i - 10i^2}{9i^2}$

$= \dfrac{-6i - 10(-1)}{9(-1)}$

$= \dfrac{-6i + 10}{-9}$

$= \dfrac{6i - 10}{9}$

$= \dfrac{-10 + 6i}{9}$

$= \dfrac{-10}{9} + \dfrac{6i}{9}$

$= \dfrac{-10}{9} + \dfrac{2i}{3}$