Solve for: (2i)/((3-i)^2)

Expression: $\frac{ 2i }{ {\left( 3-i \right)}^{2} }$

Use ${\left( a-b \right)}^{2}={a}^{2}-2ab+{b}^{2}$ to expand the expression

$\frac{ 2i }{ 9-6i+{i}^{2} }$

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

$\begin{align*}&-\frac{ 3 }{ 25 }-\frac{ 4 }{ 25 }i \\&-0.12-0.16i\end{align*}$