Respuesta :
Answer:
- [tex]\frac{2}{17}[/tex] + [tex]\frac{9}{17}[/tex] i
Step-by-step explanation:
Multiply the numerator/denominator by the complex conjugate of the denominator.
The conjugate of 1 - 4i is 1 + 4i
[tex]\frac{(2+i)(1+4i)}{(1-4i)(1+4i)}[/tex] ← expand factors
= [tex]\frac{2+9i+4i^2}{1-16i^2}[/tex] → i² = - 1
= [tex]\frac{2+9i-4}{1+16}[/tex]
= [tex]\frac{-2+9i}{17}[/tex]
= - [tex]\frac{2}{17}[/tex] + [tex]\frac{9}{17}[/tex] i
