Question

3-2i/1+4i include each step necessary in simplifying

Answer 1

Answer:

$\frac{3-2i}{1+4i}=\frac{11}{17}-\frac{10}{17}i$

Step-by-step explanation:

$\frac{3-2i}{1+4i}$ <-- Given

$\frac{3-2i}{1+4i}*\frac{1-4i}{1-4i}$ <-- Multiply by the conjugate of the denominator as a factor of 1

$\frac{(3-2i)(1-4i)}{(1+4i)(1-4i)}$

$\frac{(3)(1)+3(-4i)-2i(1)-2i(4i)}{(1)(1)+1(-4i)+4i(1)+4i(-4i)}$ <-- Use the Distributive Property and FOIL

$\frac{3-12i-2i-8i^2}{1-4i+4i-16i^2}$

$\frac{3-10i-8i^2}{1-16i^2}$

$\frac{3-10i-8(-1)}{1-16(-1)}$ <-- Rewrite $i^2$ as $-1$

$\frac{3-10i+8}{1+16}$

$\frac{11-10i}{17}$

$\frac{11}{17}-\frac{10}{17}i$ <-- Rewrite in $a\pm bi$ form