 In this video we provide the solution to question number three from the practice exam number two for math in 50 We're given two complex numbers three plus five i and one minus two i and we're asked to compute the quotient of these two Complex numbers thus writing it in the standard form a plus bi at the end So when multiplying I should say when dividing complex numbers We want to multiply the top and bottom by the conjugate of the bottom So if you have one minus two i it's conjugate We one plus two i we switch the sign of the imaginary part So we have to do that in the denominator in the numerator as well in the denominator We don't have to foil it all out Because of the way the reason we're using complex conjugation here is that when you multiply a complex number by its conjugate You're going to get a sum of squares of the real part imaginary parts So you get one squared plus negative two squared That's always how it's going to work out the denominator in the numerator a proper foil is really necessary here We're going to get three times one Which is three three times two i which is six i then we're going to get five i times one Which is a five i and then lastly we're going to get five i times two i which gives us a negative ten I took the liberty of noticing that i squared is equal to negative one All right combining like terms in the numerator. We see three minus ten is a negative seven Six i plus five i is eleven i like so and then the denominators We have one square just one and then negative two squared is a positive four like so so the denominator is going to be Five so breaking up the real part in the imaginary part We have a negative seven over five and then we have an eleven over five i like so and therefore We see that the correct answer would then be choice B