Electrical Engineering ⇒ Topic : Conjugate of a Complex Number

Conjugate of a Complex Number

Two complex numbers (or phasors) are said to be conjugate if they differ only in the algebraic sign of their quadrature components. Thus the conjugate of 2 +j 3 is 2 - j 3. The conjugate of - 4 +j 3 is - 4 - j 3. In the polar form, conjugate of 5 ∠ 30° is 5 ∠ -30° and conjugate of 10 Z 40° is 10 ∠ 40°. It is a usual practice to use an asterik (*) to indicate the conjugate.

Consider a complex number A = a + jb = A ∠ θ. Then its conjugate will be A* = a - jb =A ∠-0. The two conjugate numbers are shown graphically in Fig. (a). The conjugate numbers have the following properties

                                                figure (a)

The conjugate of a complex number is used in determining the apparent power of a circuit in complex form