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

Question

asked Dec 25, 2022 63.8k views

1 Answer

BLimitless · Answer 1 · 2023-01-01T02:46:00+0000

Answer:

(3-2i)/(1+4i)=(11)/(17)-(10)/(17)i

Explanation:

(3-2i)/(1+4i) <-- Given

(3-2i)/(1+4i)*(1-4i)/(1-4i) <-- Multiply by the conjugate of the denominator as a factor of 1

((3-2i)(1-4i))/((1+4i)(1-4i))

((3)(1)+3(-4i)-2i(1)-2i(4i))/((1)(1)+1(-4i)+4i(1)+4i(-4i)) <-- Use the Distributive Property and FOIL

(3-12i-2i-8i^2)/(1-4i+4i-16i^2)

(3-10i-8i^2)/(1-16i^2)

(3-10i-8(-1))/(1-16(-1)) <-- Rewrite
i^2 as

(3-10i+8)/(1+16)

(11-10i)/(17)

(11)/(17)-(10)/(17)i <-- Rewrite in
$a\pm bi$ form