Question

What is the quotient of 1+i/3+4i?

Answer 1

Answer:

• (7 - i) / 25

Step-by-step explanation:

Given expression:

• (1 + i) / (3 + 4i)

Multiply both sides by the conjugate of the denominator to get rid of the fraction:

• (1 + i)(3 - 4i) / (3 + 4i)(3 - 4i) =
• (3 + 3i - 4i - 4i²) / (9 - 16i²) =
• (3 - i + 4) / (9 + 16) =
• (7 - i) / 25

Answer 2

$\\ \tt\longmapsto \dfrac{1+i}{3+4i}$

• Rationalize

$\\ \tt\longmapsto \dfrac{(1+i)(3-4i)}{(3+4i)(3-4i)}$

$\\ \tt\longmapsto \dfrac{3-4i+3i-4i^2}{9-16i^2}$

$\\ \tt\longmapsto \dfrac{3-i+4}{9+16}$

$\\ \tt\longmapsto \dfrac{7-i}{25}$