Chapter 2, Problem 1RE

To determine

To calculate: The standard form of the expression $\left(8-3i\right)-\left(17-7i\right)$.

Answer to Problem 1RE

Solution:

The standard form of the expression $\left(8-3i\right)-\left(17-7i\right)$ is $-9+4i$.

Explanation of Solution

Given Information:

The provided expression is $\left(8-3i\right)-\left(17-7i\right)$.

Formula used:

If a complex number is in the form of $a+ib$ then the real part is the term which is independent of $i$ and the imaginary part is the term which is in the multiple of $i$.

Here, in the complex number $a+ib$, $a$ is the real part and $b$ is the imaginary part.

Calculation:

Consider the expression, $\left(8-3i\right)-\left(17-7i\right)$

Remove the parentheses.

$\left(8-3i\right)-\left(17-7i\right)=8-3i-17+7i$

Combine the real part and the imaginary part.

$\begin{array}{c}\left(8-3i\right)-\left(17-7i\right)=\left(8-17\right)+\left(-3i+7i\right)\\ =-9+\left(-3+7\right)i\\ =-9+4i\end{array}$

Therefore, the standard form of the expression $\left(8-3i\right)-\left(17-7i\right)$ is $-9+4i$.