Question

Simplify the expression fraction with numerator of the square root of negative four and denominator of the quantity three plus i minus the quantity two plus three times i. quantity eight plus two times i divided by seventeen quantity negative four plus two times i divided by five quantity four plus ten times I divided by twenty nine quantity eight plus ten times I divided by forty one

Answer 1

Does it look like this:
`( √(-4) )/((3+i)-(2+3i)) = (-2i)/(1-2i)` or
`(2i)/(2i-1)`

Do you need the others?

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

Answer 2

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

Explanation:

`(√(-4))/((3+i)-(2+3i))`

simplify the denominator

`(√(-4))/(1-2i)`

square root (-4) is +2i , because the value of square root (-1) is 'i'

`(+2i)/(1-2i)`

multiply top and bottom by its conjugate 1+2i

`(2i(1+2i))/((1-2i)(1+2i))`

`(2i+4i^2)/(1+2i-2i-4i^2)`

The value of i^2 =-1

`(2i+4(-1))/(1+2i-2i-4(-1))`

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

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