Question

How do you simplify $\left( 5-3i \right)+\left( 4-8i \right)$?

Answer 1

Hint: We separate the real and the imaginary parts of the equation $\left( 5-3i \right)+\left( 4-8i \right)$. We apply the binary operation of addition and subtraction for both real and the imaginary numbers. This way we solve the linear equation to find the simplified form.

Complete step by step answer:
We have been given to simplify the equation $\left( 5-3i \right)+\left( 4-8i \right)$. This consists of real and imaginary numbers. Here $i$ represents the imaginary value where $i=\sqrt{-1}$.
The given equation $\left( 5-3i \right)+\left( 4-8i \right)$ is a linear equation. We need to simplify the equation by solving the real and the imaginary numbers separately.
All the terms in the equation of $\left( 5-3i \right)+\left( 4-8i \right)$ are either real constants or an imaginary number with a coefficient. We first separate them.
$\begin{align}
  & \left( 5-3i \right)+\left( 4-8i \right) \\
 & \Rightarrow 5-3i+4-8i \\
\end{align}$
There are two such imaginary parts which are $-3i$ and $-8i$. The signs of the variables are both positive with coefficients being 5 and 4 respectively.
The binary operation between the imaginary parts is addition which gives us $-3i-8i=-11i$.
Now we take the real constants.
There are two such constants which are 4 and 5.
The binary operation between them is addition which gives us $4+5=9$.
The final solution becomes
$\begin{align}
  & 5-3i+4-8i \\
 & \Rightarrow 9-11i \\
\end{align}$.

The simplified form of $\left( 5-3i \right)+\left( 4-8i \right)$ is $9-11i$.

Note: Although simple forms of binary operations like addition, subtraction for imaginary numbers is possible as those numbers have real coefficients. But any kind of equality, inequality is not possible. Comparison between imaginary numbers is not possible.