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# complex

Create a complex number.

### Syntax

c=complex(a) c=complex(a,b)

### 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

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