Question

-2+2i / 5+3i
please help me simplify

Answer 1

do you know what a conjugate is?

Answer 2

yes

Answer 3

ok... for a complex rational, "simplify" just means, get rid of the pesky "i" in the bottom
so the way you'd do it is by multiplying both, top and bottom, by the denominator's conjugate, so
\(\bf \cfrac{-2+2i }{5+3i }\cdot \cfrac{5-3i}{5-3i}\qquad recall\implies {\color{blue}{ a^2-b^2 = (a-b)(a+b)}}\qquad thus\\ \quad \\
\cfrac{-2+2i }{5+3i }\cdot \cfrac{5-3i}{5-3i}\implies \cfrac{(-2+2i)(5-3i) }{5^2-(3i)^2 }\implies \cfrac{(-2+2i)(5-3i) }{25-3^2{\color{blue}{ i^2}} }\\ \quad \\

\cfrac{(-2+2i)(5-3i) }{25-(9\cdot {\color{blue}{ -1}}) }\)

Answer 4

okay , thanks. I understand now.

Answer 5

yw