Complex Number Complex number is of the form a + ib where a is real part and b is imaginary part. Here i = √-1
E. g.: 2 + i3; 7 + i9 etc Complex Numbers are used in many scientific fields. Two complex numbers are equal if:
o Real parts are equal o Imaginary parts are equal
E. g. Two complex numbers z1 = a + ib and z2 = c + id are equal if a = c and b = d.
Algebra of a Complex number
Addition of two complex numbers
Let z1 = a + ib and z2 = c + id be any two complex numbers. Then, z1 + z2 =( a + c) + i( b + d)
For example,( 2 + i3) +( 4 + i5) = 6 + i8 The addition of complex numbers satisfies the following properties: o o
Closure law: z1 + z2 = complex Number Commutative law: z1 + z2 = z2 + z1 o Associative law:( z1 + z2) + z3 = z1 +( z2 + z3). o Additive identity: z + 0 = z. o Additive inverse: z +(– z) = 0.
Difference of two complex numbers
Let z1 = a + ib and z2 = c + id be any two complex numbers. Then, z1- z2 =( a- c) + i( b- d)
For example,( 6 + i3) –( 2 + i) = 4 + i2