Answer:
[tex] \dfrac{7}{25} - \dfrac{1}{25}i [/tex]
Step-by-step explanation:
I assume you are asking
[tex] \dfrac{1 + i}{3 + 4i} [/tex]
although what you wrote means this
[tex] 1 + \dfrac{i}{3} + 4i [/tex]
Back to what I think is your problem:
[tex] \dfrac{1 + i}{3 + 4i} = [/tex]
[tex] = \dfrac{1 + i}{3 + 4i} \times \dfrac{3 - 4i}{3 - 4i} [/tex]
[tex] = \dfrac{(1 + i)(3 - 4i)}{(3 + 4i)(3 - 4i)} [/tex]
[tex] = \dfrac{3 - 4i + 3i - 4i^2}{9 - 16i^2} [/tex]
[tex] = \dfrac{3 - i + 4}{9 + 16} [/tex]
[tex] = \dfrac{7 - i}{25} [/tex]
[tex] = \dfrac{7}{25} - \dfrac{1}{25}i [/tex]
