Complex Conjugate

of a Complex Number is given by changing the sign of the imaginary part.
Thus, the conjugate of the complex number

z=a+ib

(where

a

and

b

are Real Number s) can be denoted by:

can also denote the Conjugate Transpose of a matrix $A$ so care must be taken not to confuse notations. If a complex number is treated as a $1 imes 1$ vector, the notations are identical.

One usually thinks of complex numbers as points in a plane with a Cartesian Coordinate System . The

x

-axis contains the real numbers and the

y

-axis contains the multiples of

i

. In this view, complex conjugation corresponds to reflection at the ''x''-axis.

In polar form, however, the conjugate of

r e^{i \phi}

is given by

r e^{-i \phi}

. This can easily be verified by using Euler's Formula .

PROPERTIES

These properties apply for all complex numbers

z

and

w

, unless stated otherwise.

	CATEGORIES ABOUT COMPLEX CONJUGATE

	complex numbers

Information About