Question

2i(4+5i)(4-5I)/4+i find the quotient and express it in its simplest form

Answer 1

The answer is B, you should really learn how to calculate these yourself though because they come up a lot.

Answer 2

Answer:

$\frac{82}{17} +\frac{328i}{17}$

Step-by-step explanation:

$\frac{2i(4+5i)(4-5i)}{4+i}$

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

$\frac{2i(4+5i)(4-5i)}{4+i}$

$\frac{2i(41)}{4+i}$

$\frac{82i}{4+i}$

Now multiply the fraction by its conjugate 4-i

$\frac{82i*(4-i)}{(4+i)(4-i)}$

$\frac{328i-82i^2}{4^2-i^2}$

$\frac{328i-82(-1)}{16-(-1)}$

$\frac{328i+82}{17}$

$\frac{82}{17} +\frac{328i}{17}$