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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

Verified Answer :

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:

\(\frac{-4+2i}{5}\)  

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

\(\frac{2i+4(-1)}{1+2i-2i-4(-1)}\)  

\(\frac{2i-4}{5}\)  

\(\frac{-4+2i}{5}\)  




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