what is -5+9i/1-i in simplest a+bi form?

Question

Express the multiplicative inverse of -5+9i divided by 1-i in simplest a+bi form

Answer 1

( - 5 + 9i)          1 + i         ( -5 + 9i)(1 + i )

------------ *  ------------ = --------------------       ( i^2 = - 1)

 1 - i                1 + i               1 - i^2

- 5 - 5i + 9i + 9 i^2                 - 5 - 5i  + 9i + 9( - 1)

----------------------------- = ---------------------------------  =

       1 - ( - 1)                                 1 + 1

(  - 14 + 4i)/2 = - 7 + 2i