Question

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

Answer 1

`\\ \tt\longmapsto (1+i)/(3+4i)`

• Rationalize

`\\ \tt\longmapsto ((1+i)(3-4i))/((3+4i)(3-4i))`

`\\ \tt\longmapsto (3-4i+3i-4i^2)/(9-16i^2)`

`\\ \tt\longmapsto (3-i+4)/(9+16)`

`\\ \tt\longmapsto (7-i)/(25)`

Answer 2

• (7 - i) / 25

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