# complex

Build an array of complex numbers from their parts

### Syntax

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

### Arguments

- u, a, b
- scalars, vectors, matrices or hypermatrices of real numbers.
If both
`a`

and`b`

are not scalars, they must have the same sizes. - c
- array of complex numbers, of the size of
`u`

or of`a`

and`b`

. If`u`

is sparse, or if`a`

and`b`

have the same sizes and both are sparse, then`c`

is also sparse. Otherwise`c`

is dense-encoded.

### Description

**c = complex(u)** creates an array
of complex numbers from their real parts `u`

,
and zero as imaginary parts.

**c = complex(a,b)** creates an array
of complex numbers from their respective real parts `a`

and their imaginary parts `b`

.

This function is equivalent to `a + imult(b)`

, which
handles properly special Inf and NaN real and imaginary parts.

### 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))

With special real or/and imaginary parts:

r = [0 0 0 %inf %inf %inf %nan %nan %nan].'; i = [0 %inf %nan 0 %inf %nan 0 %inf %nan].'; [r, i] // Then let's compare complex(r, i) with r + i*%i : [complex(r,i), r+i*%i]

--> [r, i] ans = 0. 0. 0. Inf 0. Nan Inf 0. Inf Inf Inf Nan Nan 0. Nan Inf Nan Nan // Then let's compare complex(r, i) with r + i*%i : --> [complex(r,i), r+i*%i] ans = 0. + 0.i 0. + 0.i 0. + Infi Nan + Infi 0. + Nani Nan + Nani Inf + 0.i Inf + 0.i Inf + Infi Nan + Infi Inf + Nani Nan + Nani Nan + 0.i Nan + 0.i Nan + Infi Nan + Infi Nan + Nani Nan + Nani

### History

Version | Description |

6.1.1 | Extension to sparse arrays. |

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