Answer
$7-i$
Work Step by Step
Using $a(b+c)=ab+ac$ or the Distributive Property, the given expression, $
-5(1+2i)+3i(3-4i)
,$ is equivalent to
\begin{align*}
&
-5(1)-5(2i)+3i(3)+3i(-4i)
\\&=
-5-10i+9i-12i^2
.\end{align*}
Since $i^2=-1,$ the expression above is equivalent to
\begin{align*}
&
-5-10i+9i-12(-1)
\\&=
-5-10i+9i+12
.\end{align*}
Combining the real parts and the imaginary parts, the expression above is equivalent to
\begin{align*}
&
(-5+12)+(-10i+9i)
\\&=
7+(-i)
\\&=
7-i
.\end{align*}
Hence, the simplified form of the given expression is $
7-i
$.
