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: $\frac{ \sqrt{-4} }{(3+i)-(2+3i)} = \frac{-2i}{1-2i}$ or $\frac{2i}{2i-1}$

Do you need the others?
$\frac{-4+2i}{-5} = \frac{4-2i}{5}$

Answer 2

Answer:

$\frac{-4+2i}{5}$  

Step-by-step explanation:

$\frac{\sqrt{-4}}{(3+i)-(2+3i)}$

simplify the denominator

$\frac{\sqrt{-4}}{1-2i}$

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

$\frac{+2i}{1-2i}$                    

multiply top and bottom by its conjugate 1+2i

$\frac{2i(1+2i)}{(1-2i)(1+2i)}$  

$\frac{2i+4i^2}{1+2i-2i-4i^2}$  

The value of i^2 =-1

$\frac{2i+4(-1)}{1+2i-2i-4(-1)}$  

$\frac{2i-4}{5}$  

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