Operations on Complex Numbers

We can perform addition, subtraction, multiplication, division, etc, and can also find conjugate and absolute values of complex numbers. 

• Addition:

Let a + ib and c + id be two complex numbers. The result of the addition operation is that real parts are added separately and imaginary numbers are added separately. The result is (a + c) + i(b + d). 

• Subtraction:

Let a + ib and c + id be two complex numbers. The result of the subtraction operation is that real parts are subtracted separately and imaginary numbers are subtracted separately. The result is (a – c) + i(b – d). 

• Multiplication:

Let a + ib and c + id be two complex numbers. The result of the multiplication operation is that real parts are multiplied together, imaginary parts are multiplied together and real and imaginary parts are also multiplied. The result is (a + ib)×(c+id) = ac + iad +ibc – ad.

• Conjugate:

Conjugate is nothing but changing the sign of operation in the complex number. If a + ib is a complex number than the conjugate is a – ib.

• Division:

Let a + ib and c + id be two complex numbers. We rationalize the denominator by multiplying it with its conjugate. The result is

(a + ib)/(c + id) = (a + ib)×(c – id)/(c² – d²).

• Absolute value:

The absolute value is also known as the modulus. It is the absolute value of the complex number. The absolute value of c+id is given by √c² + d²

Complex numbers are used to find the square root of negative numbers. It comprises the real and imaginary parts. The complex number is of the form a + ib where a is the real part and b is the imaginary part. The real part of the complex number is any number and is represented by Re(z) where ‘z’ is any complex number. The imaginary part of the complex number comprises any number multiplied with ‘i’, The ‘i’ stands for iota. The complex numbers cannot be represented on the number line. They are represented on a plane called Argand Plane. For example: Let z = 3 + 5i. Here Re(z) = 3 and Im(z) = 5.