Question

Write the following quotients in standard form:
(2+3i)/(4-2i)

Answer 1

you know what the conjugate of \(4-2i\) is?

Answer 2

umm not sure.

Answer 3

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

Answer 4

so to write
\[\frac{2+3i}{4-2i}\] in standard form, multiply top and bottom by \(4+2i\) and get
\[\frac{2+3i}{4-2i}\times \frac{4+2i}{4+2i}=\frac{(2+3i)(4-2i)}{4^2+2^2}\]

Answer 5

the denominator is \(20\) and the numerator is what you get when you multiply out

Answer 6

Oh I see what you are saying. Cuz you can cancel out some terms with conjugates. No wonder I didn't get the correct answer cuz I multiplied with 4-2i. Thanks for your help!

Answer 7

yw