Complex Conjugate Rules

In mathematics a number which is written in the from of p + iq is known as Complex Number. Here 'p' and 'q' are Real Numbers and 'i' is is iota symbol. The value of iota is given by:
i = √-1. In this given expression 'p' is real part and 'q' is imaginary part. Complex numbers can be used in many scientific fields such as engineering, quantum physics, applied mathematics and so on. Let's discuss different Complex Conjugate rules.
As we know that the complex number is denoted by 'Z' that contain real part and imaginary part, so we can write it as:
z = Re (z) + i im (z) = p + iq; suppose the value of Im z = 0, then the value of z = p that is a real number. If the value of Re (z) = 0 then we get z = iq that is pure Imaginary Number.
Now we will see the complex conjugate rules which are shown below:
Rule 1: Addition and subtraction:
 
The addition and subtraction rule of complex number is given by:
z₁ + z₂ = (p₁ + p₂) + i (q₁ + q₂);
Rule 2: Multiplication:
Multiplication rule is given by:
z₁ X z₂ = (p₁ + q₂) X (p₂ + i q₂) = (p₁ p₂ - q₁ q₂) + i (p₁ q₂ - p₂ q₁);
Rule 3: Division rule:
Division rule of complex number is given by:
z₁ / z₁ = (p₁ + i q₁) / (p