Question

find the quotient.write your answer in standard form: 3-i/3+i. Can someone please help me step by step

Answer 1

yes,multiply top and bottom by the conjugate of the denominator

Answer 2

so i would multiply is by 3-i?

Answer 3

the conjugate of \(a+bi\) is \(a-bi\) and this works because \[(a+bi)(a-bi)=a^2+b^2\] a real number

Answer 4

yes \[\frac{3-i}{3+i}\times \frac{3-i}{3-i}\] is the first step

Answer 5

the denominator will be \(3^2+1^2=10\) all the work is in the numerator

Answer 6

would the numerator also be 10?

Answer 7

because you would mutiply (3-i)(3=i) and get 9-3i-3i+1\[9-3i-3i+i ^{2}\]

Answer 8

and then the -3i cancel out leaving you with \[9-i ^{2}\] which is 10 right?

Answer 9

@satellite73

Answer 10

nevermind i figured it out