Addition
of Complex Number: Let z₁ = a₁ + ib₁
and z₂ = a₂ + ib₂ be two complex numbers. Then their sum z₁ + z₂ is defined as
the complex number (a₁ + a₂) + I (b₁ + b₂).
Subtraction
of Complex Number: Let z₁ = a₁ + ib₁
and z₂ = a₂ + ib₂ be two complex numbers. Then the subtraction of z₂ from z₁ is
denoted by z₁ - z₂ and is defined as the addition of z₁ and - z₂
Multiplication
of Complex Number: Let z₁ = a₁ + ib₁
and z₂ = a₂ + ib₂ be two complex numbers. Then the multiplication of z₁ with z₂
is denoted by z₁z₂ and is defined as the complex number (a₁ a₂ - b₁b₂) + i
(a₁b₂ + a₂b₁).
Division
of Complex Number: The division of a
complex numbers z₁ by a non-zero complex number z₂ is defined as the
multiplication of z₁ by the multiplicative inverse of z₂ and is denoted by z₁/z₂.
Modulus
of a Complex Number: The modulus of a
complex number z = a + ib is denoted by |z| and is defined as 
.
.
Clearly,
|z| ≥ 0 for all z ϵ C.
Example:
If z₃ = 1 + √(-3) then
Answer:
|z₃| = |1 | i√3| = 
= 2
= 2
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