Chapter I, Problem 4E

To determine

To evaluate: The expression $\left(1-2i\right)\left(8-3i\right)$ in the form of $a+bi$.

Answer to Problem 4E

The value of the expression $\left(1-2i\right)\left(8-3i\right)$ is $2-19i$.

Explanation of Solution

The product of two complex numbers defined as $\left(a+bi\right)\left(c+di\right)=\left(ac-bd\right)+i\left(ad+bc\right)$.

Thus, the expression $\left(1-2i\right)\left(8-3i\right)$ simplified as follows.

$\begin{array}{c}\left(1-2i\right)\left(8-3i\right)=\left[1\left(8\right)-\left(-2\right)\left(-3\right)\right]+i\left[1\left(-3\right)+\left(-2\right)\left(8\right)\right]\\ =\left(8-6\right)+i\left(-3-16\right)\\ =2-19i\end{array}$

Therefore, the value of the expression $\left(1-2i\right)\left(8-3i\right)$ is $2-19i$.