Respuesta :
The answer is B, you should really learn how to calculate these yourself though because they come up a lot.
Answer:
[tex]\frac{82}{17} +\frac{328i}{17}[/tex]
Step-by-step explanation:
[tex]\frac{2i(4+5i)(4-5i)}{4+i}[/tex]
First we multiply the numerator
(4+5i)(4-5i)= 16+20i-20i -25i^2
the value of i^2=-1
16 - 25(-1)= 16+25= 41
[tex]\frac{2i(4+5i)(4-5i)}{4+i}[/tex]
[tex]\frac{2i(41)}{4+i}[/tex]
[tex]\frac{82i}{4+i}[/tex]
Now multiply the fraction by its conjugate 4-i
[tex]\frac{82i*(4-i)}{(4+i)(4-i)}[/tex]
[tex]\frac{328i-82i^2}{4^2-i^2}[/tex]
[tex]\frac{328i-82(-1)}{16-(-1)}[/tex]
[tex]\frac{328i+82}{17}[/tex]
[tex]\frac{82}{17} +\frac{328i}{17}[/tex]
