Mathematical Operations with Complex Numbers

  Mathematical Operations with Complex Numbers

Complex numbers lend themselves readily to the basic mathematical operations of addition, subtraction, multipli­cation, and division. A few basic rules and definitions must be understood before considering these operations.

Let us first examine the symbol j associated with imagi­nary numbers. By definition,

Thus

j ² = -1

and    j ³ = j ²j = (-1) j = -j

with   j ⁴ = j ² j ² = (-1) (-1) = +1

          j ⁵ = j

and so on.

The reciprocal of a complex number is 1 divided by the complex number. For example, the reciprocal of

          C = A + jB     is     and of  is

Further

The conjugate or complex conjugate of a complex num­ber can be found by simply changing the sign of the imagi­nary part in the rectangular form or by negating the angle of the polar form. For example, the conjugate of