 In this video we provide the solution to question number 4 for the practice exam number 3 for Math 1060 in which case we're given a complex quotient 3 plus 5i over 2 minus 2i and we want to compute this quotient and put it in the standard complex form a plus bi. When it comes to complex quotients the strategy you should use is multiply the top and bottom by the conjugate of the denominator so you get 1 minus 2i times 1 plus 2i in the denominator you're always going to get a sum of squares so you get that is you'll take the real part squared and the imaginary part squared so you get 1 squared plus 2 squared like so and as you're squaring it doesn't matter what the sign is in the numerator though you do have to foil things out so you get 3 times 1 which is 3 3 times 2i which is 6i you're going to get 5i times 1 which is 5i and then you're going to get 5i times 2i that's going to give you a negative 10 2 times 5 is 10 and then i times i is negative 1 simplifying this the real parts in the top you get 3 minus 10 which is negative 7 for the imaginary part you're going to get 6i plus 5i which is 11i in the denominator you have a 1 plus 4 like so we do need to break it up into a real part an imaginary part the denominator turns out to be 5 so you get a negative 7 fifths and you get 11 fifths i as the final result this is the standard form in which case then we select choice B as the correct answer.