Chapter C, Problem 1E

Practice Exercises

Complex operations Let z = −2 + 5i and w = 3 – 4i. Compute the following questions.

1. z + 3w

To determine

To compute: The complex quantity $z+3w$.

Answer to Problem 1E

The value of the complex quantity $z+3w$ is $7-7i$.

Explanation of Solution

Given:

The complex values of $z=-2+5i$ and $w=3-4i$.

Calculation:

Substitute the values of $z\text{ and }w$ in the complex quantity $z+3w$ and obtain the value as,

$\begin{array}{c}z+3w=\left(-2+5i\right)+3\left(3-4i\right)\\ =-2+5i+9-12i\\ =\left(-2+9\right)+\left(5i-12i\right)\\ =7+\left(5-12\right)i\end{array}$

That is, $z+3w=7-7i$.

Therefore, the value of the complex quantity $z+3w$ is $7-7i$.