complex

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
 

See also

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

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