Question

Calcule: $\frac{5+5i}{3-4i} + \frac{20}{4+3i}$

Answer 1

Primeira parte:

$\frac{5+5i}{3-4i}.\frac{3+4i}{3+4i} = \frac{15 + 20i + 15i + 20i^2}{9+16} = \frac{-5 + 35i}{25}$

Segunda parte:

$\frac{20}{4+3i}.\frac{4-3i}{4-3i} = \frac{80 - 60i}{16 + 9} =\frac{80 - 60i}{25}$

Somando as duas partes temos:

$\frac{-5 + 35i}{25} + \frac{80 - 60i}{25} = \\\\ \frac{75 - 25i}{25} = \\\\ \frac{75}{25} - \frac{25}{25}i = \\\\3 - i$ 

;)