Introduction and Operations with Complex Numbers
by A number of the form a + ib where a,b belong to set of real numbers and I = square root of -1, is called complex numbers. A complex number is defined as a ordered pair of real numbers a and b, and may be written as (a,b),where the first number denotes real part and second number denotes imaginary part. We denote the set of Complex numbers with “C”.
OPERATIONS WITH COMPLEX NUMBERS
EQUALITY OF TWO COMPLEX NUMBERS :
Two Complex Numbers Z(1) = a + ib and Z(2) = c + id are said to be equal if a = c and b = d
ADDITION OF TWO COMPLEX NUMBERS :
Suppose there exists two complex numbers Z(1) and Z(2) such that Z(1) = a + ib and Z(2) = c + id then the sum of these two complex numbers (i.e) Z(1) + Z(2) = a + ib + c + id = (a + c) + i(b + d).
SUBSTRACTION OF TWO COMPLEX NUMBERS :
Consider two complex numbers Z(1)= a + ib and Z(2)= c + id then the difference Z(1) – Z(2) = (a – c) + i (b – d).
MULTIPLICATION OF COMPLEX NUMBERS :
Again let Z(1) = a + i b and Z(2)= c + i d then Z(1) * Z(2) = (a + ib) * (c + id = (ac – bd) + i (ad + bc)
QUOTIENT OF TWO COMPLEX NUMBERS :
If atleast one of c,d is non zero,then quotient of a + ib and c + id is given by
(a + ib)/(c + id) = (a + ib)*(c + id)/(c + id)*(c – id) = {(ac + bd) + i(bc – ad)}/[{(c + d)*(c + d)} - 2cd]
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