Question

Quotient of 1+i/3+4i?

Answer 1

Answer:

$\dfrac{7}{25} - \dfrac{1}{25}i$

Step-by-step explanation:

I assume you are asking

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

although what you wrote means this

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

Back to what I think is your problem:

$\dfrac{1 + i}{3 + 4i} =$

$= \dfrac{1 + i}{3 + 4i} \times \dfrac{3 - 4i}{3 - 4i}$

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

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

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

$= \dfrac{7 - i}{25}$

$= \dfrac{7}{25} - \dfrac{1}{25}i$