## Precalculus (6th Edition) Blitzer

The standard form of the expression $\left( -5+4i \right)\left( 3+i \right)$ is $-19+7i$.
Consider the expression $\left( -5+4i \right)\left( 3+i \right)$. Use the FOIL method. $\left( -5+4i \right)\left( 3+i \right)=-15-5i+12i+4{{i}^{2}}$ Replace the value ${{i}^{2}}=-1$. $\left( -5+4i \right)\left( 3+i \right)=-15-5i+12i+4\left( -1 \right)$ Make a group of real and imaginary terms. $\left( -5+4i \right)\left( 3+i \right)=-15-4+12i-5i$ Simplify the real and imaginary terms. \begin{align} & \left( -5+4i \right)\left( 3+i \right)=\left( -15-4 \right)+\left( 12-5 \right)i \\ & =-19+7i \end{align} Therefore, the standard form of the expression $\left( -5+4i \right)\left( 3+i \right)$ is $-19+7i$.