Respuesta :
Answer:
[tex]\frac{3-2i}{1+4i}=\frac{11}{17}-\frac{10}{17}i[/tex]
Step-by-step explanation:
[tex]\frac{3-2i}{1+4i}[/tex] <-- Given
[tex]\frac{3-2i}{1+4i}*\frac{1-4i}{1-4i}[/tex] <-- Multiply by the conjugate of the denominator as a factor of 1
[tex]\frac{(3-2i)(1-4i)}{(1+4i)(1-4i)}[/tex]
[tex]\frac{(3)(1)+3(-4i)-2i(1)-2i(4i)}{(1)(1)+1(-4i)+4i(1)+4i(-4i)}[/tex] <-- Use the Distributive Property and FOIL
[tex]\frac{3-12i-2i-8i^2}{1-4i+4i-16i^2}[/tex]
[tex]\frac{3-10i-8i^2}{1-16i^2}[/tex]
[tex]\frac{3-10i-8(-1)}{1-16(-1)}[/tex] <-- Rewrite [tex]i^2[/tex] as [tex]-1[/tex]
[tex]\frac{3-10i+8}{1+16}[/tex]
[tex]\frac{11-10i}{17}[/tex]
[tex]\frac{11}{17}-\frac{10}{17}i[/tex] <-- Rewrite in [tex]a\pm bi[/tex] form
