Question

How do you simplify $6-\left( 8+3i \right)?$

Answer 1

Hint: For simplifying the terms given in the question, add or subtract the real numbers with real numbers and imaginary numbers by imaginary number, then rewrite the obtained number in for of real number $+/-$ imaginary number or in form of complex number.

Complete step by step solution:
As per data given in the question,
As we have to simplify $6-\left( 8+3i \right)$
As here, first number is $6$
So, for simplifying the numbers, let’s convert $6$ in form of a complex number.
A complex number is a combination of real and imaginary numbers.
As in 6 there is no imaginary part,
So, we will consider $6$ as $6+0i$
Now, simplifying the given terms,
We have.
$6-\left( 8+3i \right)=\left[ \left( 6+0i \right)-\left( 8+3i \right) \right]$
For simplifying the terms,
We need to add or subtract the real part with the real part and the imaginary part with the imaginary part.
So, $6$ will be simplified with $8$ and $0i$ will be simplified with $3i$
So,
We will get,
$\Rightarrow \left[ \left( 6+0i \right)-\left( 8+3i \right) \right]$
$\Rightarrow \left[ 6+0i-8-3i \right]$
$\Rightarrow \left[ 6-8+0i-3i \right]$
$\Rightarrow \left[ -2-3i \right]$
$\Rightarrow -\left( 2+3i \right)$
Hence,
We can say that,
After simplifying the values given in the question,
We will get, $\left[ -2-3i \right]$ or $-\left( 2+3i \right)$

Note: Complex numbers are such numbers which are written in form of $a+ib$
Here, $''a''$ is real number, as real numbers are those numbers whose values starts from zero to infinity, while imaginary numbers are normally written in form of $''i''$
When,
We need to convert imaginary number in form of real number, we need to multiply it by $''i''$
When we multiply $''i''$ by $''i''$ it will be equal to $-1.$
So, we can say that,
When $''3i''$ is converted in form of real number,
Then it will be equal to $''3i\times i''=3{{i}^{2}}=3\times \left( -1 \right)=-3$
Hence, by this way we can convert imaginary numbers in the form of real numbers.
While simplifying the terms make sure that you are simplifying the real numbers with only real numbers and imaginary numbers with only imaginary numbers.
When the numbers which are subtracted are written in the equation then make sure you are reversing the sign of the values of quantity which is to be subtracted, like when $\left( 8+3i \right)$ is subtracted then the sign of the number will get reversed as $\left( -8-3i \right)$