Thursday, July 25

# Complex Number- Definition

Mathematics deals with different types of numbers. There are real numbers, whole numbers, and many more. real numbers have definite tangible values and can be countable. Examples of real numbers are fractions, integers, etc. There is a special type of number that can be represented as a combination of a real number and an imaginary number. It is called a complex number . The expression of a complex number is in the format of p +iq. We can see a complex number has two parts. Here p is the real number part and iq is the imaginary number part. Actually, q is also a real number that is multiplied by an imaginary number ‘I’ to form an Imaginary number part. An imaginary number is that number that gives a negative value when its square root is done. It is to be noted that the term complex does not indicate complicated but it implies that complex numbers are formed as a building block or complex by a combination of two types of numbers.

## Example of a Complex Number

A complex number is denoted as an addition of two numbers, in the form of z= a + ib, where both a and b are real numbers and i is an imaginary number. The imaginary number ‘i’ is termed as ‘iota’ which has a value equal to √-1. For example, 5+8i is a complex number where 5 is a real number part and 8i is an imaginary number part. The imaginary part is formed by multiplying the real number 8 by the imaginary number i (= √-1). The number 0 is a real number as well as a complex number because it can be written in the format of 0+0i. So, zero is the only real number that can also be considered as a complex number .

## Points of Complex Numbers

• For the complex number that equals zero, both the real part and the imaginary part are zero.
• If a + ib and c + id are two complex numbers that are equal to each other and a, b, c, and d are real numbers then a = c, and b = d
• The commutative law of addition and multiplication is applicable for complex numbers .

## Arithmetic Operations Involving Complex Numbers

Addition and subtraction of complex numbers can be done by separately combining similar parts. This means the addition or subtraction of real numbers is done with the real number and imaginary number with the imaginary number to get the result.

For example, (a + ib) + (c + id) = (a + c) + i(b + d) and (a + ib) – (c +id) = (a– c) + i(b – d)

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