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