Conjugates of Complex Numbers - Practice Questions & MCQ

The conjugate of a complex number z = a + ib (a, b are real numbers) is a − ib. It is denoted as  .

i.e. if z = a + ib, then its conjugate is   = a - ib.

Conjugate of complex numbers is obtained by changing the sign of the imaginary part of the complex number. The real part of the number is left unchanged.

Note: 

• When a complex number is added to its complex conjugate, the result is a real number. i.e. z = a + ib,   = a - ib

            Then the sum, z + = a + ib + a - ib = 2a (which is real)

• When a complex number is multiplied by its complex conjugate, the result is a real number i.e. z = a + ib,  = a - ib

            Then the product, z・ = (a + ib)・(a - ib) = a² - (ib)²

                                                  = a² +  b² (which is real)

Geometrically complex conjugate of a complex number is its mirror image with respect to the real axis (x-axis).

For example

z = 2 + 2i   and  =  2 - 2i

Properties of the conjugate complex numbers:

z, z₁, z_2, and z₃ be the complex numbers