Answer
$\displaystyle \frac{-44}{157}-\frac{24}{157}i$
Work Step by Step
$\displaystyle \frac{4i}{-6-11i}\qquad$ ...rationalize by multiplying both the numerator and denominator with $-6+11i$.
$=\displaystyle \frac{4i(-6+11i)}{(-6-11i)(-6+11i)}\qquad$ ...use the FOIL method.
$=\displaystyle \frac{-24i+44i^{2}}{(-6-11i)(-6+11i)}\qquad$ ...difference of squares: $(a+b)(a-b)=a^{2}-b^{2},a=-6, b=11i$
$==\displaystyle \frac{-24i+44i^{2}}{(-6)^{2}-(11i)^{2}}\qquad$ ...simplify. ($i^{2}=-1$)
$=\displaystyle \frac{-24i-44}{36+121}\qquad$ ...add like terms.
$=\displaystyle \frac{-44-24i}{157}\qquad$ ...write in standard form.
$=\displaystyle \frac{-44}{157}-\frac{24}{157}i$
