Question

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

A; 82/16+32/17i

B: 82/17+328/17i

C: 82/16-308/16i

D: 1/3+11/3i

Answer 1

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

Answer 2

`(82)/(17) +(328i)/(17)`

Explanation:

`(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

`(2i(4+5i)(4-5i))/(4+i)`

`(2i(41))/(4+i)`

`(82i)/(4+i)`

Now multiply the fraction by its conjugate 4-i

`(82i*(4-i))/((4+i)(4-i))`

`(328i-82i^2)/(4^2-i^2)`

`(328i-82(-1))/(16-(-1))`

`(328i+82)/(17)`

`(82)/(17) +(328i)/(17)`