Chapter I, Problem 3E

To determine

To evaluate: The expression $\left(2+5i\right)\left(4-i\right)$ in the form of $a+bi$.

Answer to Problem 3E

The value of the expression $\left(2+5i\right)\left(4-i\right)$ is $13+18i$.

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 $\left(2+5i\right)\left(4-i\right)$ simplified as follows.

$\begin{array}{c}\left(2+5i\right)\left(4-i\right)=\left[2\left(4\right)-5\left(-1\right)\right]+i\left[2\left(-1\right)+5\left(4\right)\right]\\ =\left(8+5\right)+i\left(-2+20\right)\\ =13+18i\end{array}$

Therefore, the value of the expression $\left(2+5i\right)\left(4-i\right)$ is $13+18i$.