Question

Simplify the given expression:
4/3-2i

Answer 1

the way you'd do it is by multiplying both top and bottom by the "conjugate" of the denominator

Answer 2

so basically the opposite
4*3+2i like that

Answer 3

\(\bf \cfrac{4}{3-2i}\qquad conjugate\ of\ 3-2i\to 3+2i
\\ \quad \\
\cfrac{4}{3-2i}\cdot \cfrac{3+2i}{3+2i}\implies \cfrac{4(3+2i)}{(3-2i)(3+2i)}
\\ \quad \\
recall\implies {\color{brown}{ (a-b)(a+b) = a^2-b^2}}\qquad thus
\\ \quad \\
\cfrac{4(3+2i)}{(3-2i)(3+2i)}\implies \cfrac{4(3+2i)}{3^2-(2i)^2}\implies \cfrac{4(3+2i)}{3^2-2^2i^2}\)

expand the bottom and simplify
keep in mind that \(\bf i^2\to -1\)

Answer 4

alright thanks you helped me a lot
so the answer is 12+8i/13