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# 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
```

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

### History

 Version Description 6.1.1 Extension to sparse arrays.