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BodhiAI1
Nov. 11, 2019

Addition ,subtraction, multiplication and division of complex numbers:

Addition of Complex Numbers 

Let and be two complex numbers. Then their sum z, is defined as

where,

Re(z) =

Also, IM(z) =

Properties of Addition of Complex Numbers

P-1 Addition is Commutative

For any two complex numbers and we have 

p-2 Addition is Associative

For any three complex numbers and we have 

P-3 Existence of Additive Identity

The complex number z = 0 + 0 is the identity element for addition, because adding zero to any quantity does not changes the value (identity) of the quantity to which it was added, i.e.

z + 0 = z = 0 + z  

Subtraction of Complex Numbers

Let and be any two complex numbers. Then the subtraction of z1 from z2 is defined as the addition of z1 with the additive inverse of z2 and is denoted as

where, Re

and Im

Important

a) Properties of subtraction is analogous to Properties of Addition of Complex Numbers.

b) As subtraction of two complex numbers is equivalent to addition of first with the additive inverse of second.

Multiplication of Complex Numbers

Let and be two complex numbers. Then the multiplication of with is defined as

Important

Multiplication as the set of ordered pair.

Properties of Multiplication

P-1 Multiplication is Commulative

For any two complex numbers z1 and z2, we have 

P-2 Multiplication is Associative

For any three complex numbers and we have

P-3 Existence of Multiplicative Identity

The complex number z = 1+ is the identity element for multiplication, because multiplying any quantity by 1 does not changes the value (identity) of that quantity, i.e.

z.1 = z =1. z zC

Division of Complex Numbers

The division of complex number by a non-zero complex number is defined as multiplication of with the multiplicative inverse of z2 such that

Important 

a) Properties of Division is analogous to Properties of Multiplication of Complex Numbers.

b) As division of two complex numbers is equivalent to multiplication of first with multiplicative inverse of second.