Question

How do you perform the operation and write the result in standard form given $\left( {8 - i} \right) - \left( {4 - i} \right)$?

Answer 1

Here we have to find the value of $(8 - i) - (4 - i)$ by using the simple arithmetic operations. Since the number is of the complex number where it contains both real part and imaginary part. We will use the concept of sign conventions and arithmetic operations and determine the value.

Complete step-by-step solution:
In mathematics we have different kinds of numbers namely, natural numbers, whole numbers, integers, real numbers, complex numbers, rational numbers, irrational numbers. The arithmetic operations are of 4 kinds namely, addition, subtraction, multiplication and division.The given number is a complex number and it contains both the real part and imaginary part. The “$i$” in the number represents the imaginary.

Now consider the given question
$\Rightarrow \left( {8 - i} \right) - \left( {4 - i} \right)$
On applying the sign conventions, where when minus sign is multiplied minus sign then we obtain plus sign and the above equation is written as
$\Rightarrow 8 - i - 4 + i$
Since we have -I and +I, it will get cancelled. Therefore the above equation is written as
$\Rightarrow 8 - 4$
On subtracting 4 from 8 we get 4. Therefore the result is
$\Rightarrow 4$
Hence we have solved the given complex number and obtained the solution for the given question.

Therefore the answer for the given question is 4

Note: A complex number is a combination of real number and the imaginary number where $i$ represents the imaginary. “$i$” is the imaginary part $i = \sqrt { - 1}$ and also ${i^2} = - 1$. We must know about the sign conventions and we have used simple subtraction arithmetic operations. hence these problems are solved in the above manner itself.