Question

3+2i/1-2i I know I'm lame, I ended up with the answer -1+8i/5 I know that can't be right, can someone please help

Answer 1

idea is to multiply top and bottom by the conjugate of the denominator
the conjugate of \(a+bi\) is \(a-bi\) so the conjugate of \(1-2i\) is \(1+2i\)

Answer 2

this works because \((a+bi)(a-bi)=a^2+b^2\) a real number
in your case \((1+2i)(1-2i)=1^2+2^2=1+4=5\)
that will be your denominator

Answer 3

the work looks like
\[\frac{3+2i}{1-2i}\times \frac{1+2i}{1+2i}=\frac{(3+2i)(1+2i)}{5}\] so now it is left to multiply out up top

Answer 4

ok so u end up with a numerator of 3+8i+4i^2?

Answer 5

so you end up with a real number answer of -9/5?