COMPLEX NUMBER
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A complex number:
Complex number is a combination of real and imaginary numbers.
For example a complex number may be denoted as
Z = a + ib
Here Real and Imaginary part can split as
Re_Z = a
Im_Z= b
Example of complex No: (10 +15i)
Re_Z = 10
and, Im_Z = 15
Modulus or Absolute Value of a Complex number
Modulus Or Absolute Value of a complex number can be denoted by |z| and is defined as below :
|z| = v(a2 + b2 ) = Sqrt(a2 + b2 )
Example: Find the modulus of Z = 7 +5i
Modulus of z = |z| = v(72 + 52) = v74
Operations in Complex Numbers
Sum of complex number: For two complex number z1 = a+ib and z2 = c + id
z1 + z2 = (a + ib) + (c + id)
or simply z1 + z2 = (a + c) + i( b + d)
Difference of complex number: For two complex number z1 = a+ib and z2 = c + id z1 - z2 = (a + ib) - (c + id)
or simply z1 - z2 = (a - c) + i( b - d)
Product of complex number: For two complex number z1 = a+ib and z2 = c + id
z1 x z2 = (a + ib) (c + id)
or simply z1 xz2 = (ac - bd) + i( ad + bc)
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