Question

how would i express the following quotient that is attached in a+bi form?

Answer 1

\[\frac{ 5-2i }{ 3+2i }\]

Answer 2

multiply top and bottom by conjugate.

For a+bi the conjugate is a-bi

So for 3+2i the conjugate is ?

Answer 3

is a conjugate 2i ?

Answer 4

in your case the conjugate is 3-2i.

Multiply top and bottom times 3-2i and show me what you get.

Answer 5

\[\frac{ 5-2i }{ 3+2i }\times \frac{3-2i}{3-2i}=\frac{(5-2i)(3-2i)}{3^2+2^2}\] is a start

Answer 6

this because \[(a+bi)(a-bi)=a^2+b^2\]
now the denominator is a real number

Answer 7

since \(3^2+2^2=9+4=13\) your only real job is to multiply
\[(5-2i)(3-2i)\]for the top
do you know how to do that?

Answer 8

i only know how to do that as F.O.I.L

Answer 9

ok that works

Answer 10

\[(5-2i)(3-2i)=15-10i-6i+4i^2\] if you use that method
then since \(i^2=-1\) you get
\[15-4-16i=11-16i\]

Answer 11

making your final answer
\[\frac{11-16i}{13}=\frac{11}{13}-\frac{16}{13}i\]

Answer 12

if you are going to do more than two or three of these, it might help to know what
\[(a+bi)(c+di)=(ac-bd)+(ad+bc)i\]but "foil" works just as well, if you remember that \(i^2=-1\)

Answer 13

ok, thank you so much for walking me through this problem, ill take this problem down into my notes for future reference :)

Answer 14

yw