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)

Complex Function 复变函数

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().

Complex

complex - complex function - complex math
complex animate(z) or complex2D(x) for phase animation in complex plane, the independent variable must be z.
complex plot(z) for phase and/or modulus in complex plane, the independent variable must be z.
plot complex(z) for phase and/or modulus in complex plane, the independent variable must be z.
complex2D show re2D(x) and im2D(x) for complex 2 curves of real and imag parts in real and imag domain, 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

References

math handbook content 2 chapter 10 complex function
math handbook content 3 chapter 10 complex function
math handbook content 4 chapter 10 complex function
Complex analysis