Answer:
[tex]\frac{-4+2i}{5}[/tex]
Step-by-step explanation:
We are given the expression, [tex]\frac{\sqrt{-4}}{(3+i)-(2+3i)}[/tex]
On simplifying, we have,
[tex]\frac{2i}{3+i-2-3i}[/tex]
i.e. [tex]\frac{2i}{1-2i}[/tex]
Now, we will rationalize the expression,
i.e. [tex]\frac{2i}{1-2i}\times \frac{1+2i}{1+2i}[/tex]
i.e. [tex]\frac{(2i)\times (1+2i)}{(1-2i)\times (1+2i)}[/tex]
i.e. [tex]\frac{2i+4i^{2}}{1-4i^{2}}[/tex]
Since, [tex]i^{2}=-1[/tex], we get,
i.e. [tex]\frac{2i-4}{1+4}[/tex]
i.e. [tex]\frac{-4+2i}{5}[/tex]
So, the simplified expression is [tex]\frac{-4+2i}{5}[/tex].
