complex

Arguments

a

a 1-by-1 or a n-by-m real matrix of doubles, the real part. If a has an imaginary part, an error is generated.

b

a 1-by-1 or a n-by-m real matrix of doubles, the imaginary part (default b=0). If b has an imaginary part, an error is generated.

c

a n-by-m complex matrix of doubles, the complex number.

Description

c=complex(a) creates a complex number from its real part a and zero as the imaginary part.

c=complex(a,b) creates a complex number from its real part a and imaginary part b.

This function is a substitute for expressions such as a+%i*b, especially in cases where the complex arithmetic interferes with particular floating point numbers such as %inf or %nan.

Examples

In the following example, we create a complex number from its real and imaginary parts.

complex(1,2)
complex([1 2],[3 4])

If a only is specified, then the imaginary part is set to zero.

complex([1 2 3])

If a is a scalar and b is a matrix, then the result c has the same size as b. Similarly, if b is a scalar and a is a matrix, then the result c has the same size as a.

c = complex([1 2 3], 4)
c = complex(1, [2 3 4])

If a and b are two matrices with different sizes, an error is generated, as in the following session.

-->complex(ones(2,3),ones(4,5))
 !--error 10000
complex: Incompatible input arguments #1 and #2: Same sizes expected.
at line      33 of function complex called by :
complex(ones(2,3),ones(4,5))
 

The purpose of the complex function is to manage IEEE floating point numbers such as Nans or Infinities. In the following example, we show that creating a complex number where the real and imaginary parts are complex is not straightforward if we use the complex arithmetic. This is because the product %i times %inf is evaluated as (0+%i) * (%inf+%i*0). This produces the intermediate expression 0*%inf, which is %nan.

-->%inf+%i*%inf
 ans  =
    Nan + Inf
 

The solution of this issue is to use the complex function.

-->complex(%inf,%inf)
 ans  =
    Inf + Inf
 

See also

• %i — imaginary unit
• imult — multiplication by i the imaginary unitary