Question

Números complexos

Calcule os seguintes quocientes: a) 6/1+i
B) 1-3i/i-1
c) 3-4i/i+2

Answer 1

$A) \frac{6}{1+i} = \frac{6}{1+i} \cdot\frac{1-i}{1-i} =\frac{6-6i}{1-i+i-i^2}=\frac{6-6i}{2}=3-3i\\\\ B) \frac{1-3i}{i-1} = \frac{1-3i}{i-1} \cdot\frac{i+1}{i+1}=\frac{i+1-3i^2-3i}{i^2+i-i-1}=\frac{4-2i}{-2}=-2+i\\\\ C) \frac{3-4i}{i+2}=\frac{3-4i}{i+2}\cdot\frac{i-2}{i-2}=\frac{3i-6-4i^2+8i}{i^2-2i+2i-4}=\frac{-2+11i}{-5}=\frac{2}{5}-\frac{11}{5}i$