Complex Numbers

 

Complex number

The number of the form a + ib, where a and b are real number and i² = ­-1, is called a complex number. The complex number is generally is denoted by z or w and it can also be written as ordered pair form (a, b).

\ z = a + ib = (a, b).

In complex number z = a + ib, a is called the real part and b is called the imaginary part and it can be written as a = Re (z) and b = Im(z)

Properties of complex number

·      If z₁ = (a, b) and z₂ = (c, d), then

      z₁ + z₂ = (a + c, b + d) (sum of complex numbers)

      z₁z₂ = (ac - bd, ad + bc) (product of complex numbers)

Imaginary unit

    The complex number (0, 1) i.e. the complex number where real part is zero and the imaginary part is unity is called the imaginary unit. It is denoted by i, so i = (0, 1).

Conjugate of complex number

The conjugate of a complex number z = a + ib = (a, b) is denoted by z and is defined by z = a - ib.