Complex Number Functions

Functions > Utility Functions > Complex Number Functions

Magnitude and Argument

• Re(Z)—Returns the real part of Z.

• Im(Z)—Returns the imaginary part of Z.

• arg(z)—Returns the principal argument of z, between −π and π, including π. The argument is the value of θ when z is written as |z| · e^(i·θ).

The arg function is related to the polar angle functions.

Sign

• csgn(z)—This function is used to determine in which half-plane (left or right) the complex-valued expression or number z lies. It returns the following results:

Argument	Result
z = 0	0
Re(z) > 0 or (Re(z) = 0 and Im(z) > 0)	1
Otherwise	−1

• signum(z, [x])—This vectorized function returns the sign of a real or complex number. It returns the following results:

Argument	Result
z = 0	x
z = 0	1 if x is omitted.
z ≠ 0	z/\|z\|

◦ z and x can be any combination of scalar and vector.

◦ If z and x are both vectors, then they must have the same dimension.

• sign(x)—This function returns the sign of a real number. It returns the following results:

Argument	Result
x = 0	0
x > 0	1
Otherwise	−1

Arguments

• Z is a real or complex scalar or matrix.

• z is a real or complex scalar or vector.

• x is a real scalar or vector.