$\frac{ 2i }{ 9-6i+{i}^{2} }$
By definition ${i}^{2}=-1$$\frac{ 2i }{ 9-6i-1 }$
Subtract the numbers$\frac{ 2i }{ 8-6i }$
Factor out $2$ from the expression$\frac{ 2i }{ 2\left( 4-3i \right) }$
Cancel out the common factor $2$$\frac{ i }{ 4-3i }$
Divide the complex numbers$-\frac{ 3 }{ 25 }+\frac{ 4 }{ 25 }i$
To find the conjugate of a complex number $a+bi$, change the sign of the imaginary part$\begin{align*}&-\frac{ 3 }{ 25 }-\frac{ 4 }{ 25 }i \\&-0.12-0.16i\end{align*}$