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.
[tex] \dfrac{-6 - 10i} {9i } \times \dfrac{i}{i} = [/tex]
[tex] = \dfrac{(-6 - 10i)i}{(9i)i} [/tex]
[tex] = \dfrac{-6i - 10i^2}{9i^2} [/tex]
[tex] = \dfrac{-6i - 10(-1)}{9(-1)} [/tex]
[tex] = \dfrac{-6i + 10}{-9} [/tex]
[tex] = \dfrac{6i - 10}{9} [/tex]
[tex] = \dfrac{-10 + 6i}{9} [/tex]
[tex] = \dfrac{-10}{9} + \dfrac{6i}{9} [/tex]
[tex] = \dfrac{-10}{9} + \dfrac{2i}{3} [/tex]
