Question

How do you simplify $\left( -4-2i \right)-\left( -2+3i \right)?$

Answer 1

Hint: Here, a linear equation is given which we have to simplify but not to solve. For that, first we have to remove all parentheses from the equation.
Then put the like term together and combine them.
Solve the like terms.
We will get the simplified equation after solving it.

Complete step-by-step answer:
Given that, there is a linear equation as follow,
$\Rightarrow$$\left( -4-2i \right)-\left( -2+3i \right)$
Now, remove all the brackets and rewrite the above equation.
After removing all parenthesis the equation becomes.
$\Rightarrow$$-4-2i+2-3i$
Now, write the like terms together
$\Rightarrow$$-4+2-2i-3i$
Now, group and combine the like terms
$\Rightarrow$$\left( -4+2 \right)+\left( -2-3 \right)i$
Solve the above brackets
$\Rightarrow$$-2+\left( -5 \right)i$
$\Rightarrow$$-2-5i$

Therefore the simplified form of the given equation is $-2-5i$.

Additional Information:
The equation which has only one variable then that equation is called as one variable linear equation. The one variable linear equation can be expressed in the following form.
$\Rightarrow$$ax+b=0$
Where, $a$ and $b=$ two integers or number.
$x=$ variable
This type of equation has only one solution.
For example $2x-4=0$
In general the linear equation is that equation which is used for showing the lines in a coordinate system whereas the general form of the linear equation for straight lines is:
$\Rightarrow$$y=mx+b$
Where, $m=$ slope of the line
$b=$$y$-intercept
The linear equation has only one as a highest variable exponent.
There are some forms of linear equation for representing it, such as,
> General form,
> Slope-intercept form
> Point form
> Intercept form
> Two point form.

Note:
In this numerical, we have to just simplify the given equation rather than to solve and find the solution.
So, for simplifying the given equation, we have to remove the parentheses.
While removing parentheses we must have to be careful about the signs of every individual term.
Otherwise a common mistake in the equation can change the whole equation.
The given equation can be simplified in another way also which is as follows:
We know that, a complex number is consist of $2$ parts that is real parts Re-and an imaginary part $\operatorname{Im}.$
So, the common structure will become as,
$\operatorname{Re}+\operatorname{Im}$
The given equation is,
$\left( -4-2i \right)-\left( -2+3i \right)$
So, now using above structure of columnar subtraction or addition, we get
$=-2-5i$
As, given in question that is the subtraction of two terms, therefore we are doing here subtraction.
Thus, the final simplified equation is $-2-5i$.