Answer
$-11+29i$
Work Step by Step
Multiplication of complex numbers works just like for polynomials
\begin{align*}(2+3i)(5+7i)=&2(5+7i)+3i(5+7i)~~~\text{Distributive property}\\
=&2(5)+2(7i)+3i(5)+3i(7i)~~~\text{Simplify}\\
=&10+14i+15i+21i^2\\
=&10+29i+21(-1) ~~~~\because i^2=-1\\
=&10-21+29i~~~~~\text{Simplify}\\
=&-11+29i
\end{align*}
The Cartesian form of $(2+3i)(5+7i)$ is $-11+29i$.
