# Complex 复数

Complex numbers are represented by a dictionary of real and imaginary attributes:

**complex( ***x*, *y* ) — returns a complex number as `{ re: `*x*, im: *y* }

**complex( ***x* ) — returns a complex number as `{ re: `*x*, im: 0 }

## Real and imaginary part

The separate attributes can be accessed through their respective names,
complex( *x*, *y* ).re = *x*
complex( *x*, *y* ).im = *y*

or with convenience functions:

**re( ***x* ) — real part of a real or complex number

**real( ***x* ) — real part of a real or complex number

**im( ***x* ) — imaginary part of a real or complex number

**imag( ***x* ) — imaginary part of a real or complex number

## Operator

Since JavaScript does not support operator overloading, functions are available for complex arithmetic:
**add( ***x*, *y* ) — add two real or complex numbers of x+y

**add( ***x*, *y*, *z*, … ) — add an arbitrary number of real or complex numbers of x+y+z

**sub( ***x*, *y* ) — subtract two real or complex numbers of x-y

**mul( ***x*, *y* ) — multiply two real or complex numbers of x*y

**mul( ***x*, *y*, *z*, … ) — multiply an arbitrary number of real or complex numbers of x*y*z

**div( ***x*, *y* ) — divide two real or complex numbers of x/y

**neg( ***x* ) — negate a real or complex number of -x

**inv( ***x* ) — invert a real or complex number of 1/z

**pow( ***x*, *y* ) — power two real or complex numbers of x^y

**root( ***x*, *y* ) — root two real or complex numbers of x^(1/y)

## Computation

Please convert to complex() and complex operator by tocomplex() before complex computation.
Plot complex function for the real domain x by complex2D(), and for complex domain by complex3D().
## References

- complex
- complex function
- complex math
- math handbook chapter 10 complex function
- complex animate(z) for phase animation, the independent variable must be z.
- complex plot(z) for phase and/or modulus, the independent variable must be z.
- complex2D(x) for complex 2 curves of real and imag parts, the independent variable must be x.
- complex3D(x) for 3 dimensional graph, the independent variable must be x.
- color WebXR surface of complex function on complex plane
- Riemann surface
- Complex Branches
- complex coloring
- 2D surface
- 3D surface