conj

Complex conjugate of symbolic input

Syntax

conj(x)

Description

conj(x) returns the complex conjugate of x. Because symbolic scalar variables are complex by default, unresolved calls, such as conj(x), can appear in the output of norm, mtimes, and other functions. For details, see Use Assumptions on Symbolic Variables.

For complex x, conj(x) = real(x) - i*imag(x).

Examples

Conjugate of Numeric and Symbolic Input

Compute the conjugate of numeric input.

conj(1+3i)

ans =
   1.0000 - 3.0000i

Compute the conjugate of symbolic input.

syms x
f = x^2;
fConj = conj(f)

fConj =
conj(x)^2

Convert symbolic output to double by substituting for x with a number by using subs, and then using double.

fConj = subs(fConj,x,1+2i);        % x is 1+2i
fConj = double(fConj)

fConj =
  -3.0000 - 4.0000i

Conjugate of Real Inputs Using Assumptions

If the input is real, conj returns the input instead of an unresolved call. Assume x is real and find its conjugate. conj returns x instead of conj(x), as expected.

syms x
assume(x,'real')
conj(x)

ans =
x

Clear the assumption for further computations.

assume(x,'clear')

Input Arguments

x — Input

number | vector | matrix | array | symbolic number | symbolic scalar variable | symbolic matrix variable | symbolic array | symbolic function | symbolic expression

Input, specified as a number, vector, matrix, or array, or a symbolic number, scalar variable, matrix variable (since R2021a), array, function, or expression.