Complex Number Library

This is a complex number libry that can perform some simple operations of complex number. To use it, the libry has to be required in your code. You can use

var Complex = require("Complex")

Complex constructor:

var z = new Complex(real, im);

Arguments:

1. real (number) the real part of the number
2. im (number) the imaginary part of the number

Function: Complex.from: An in line function like Number.from. var z = Complex.from(real[, im]);

Arguments:

1. real (number): the real part of the number
2. im (number, optional): the imaginary part of the number Or
3. real (string): a string representation of the number, for example 1+4i

Examples:

var z = Complex.from(2, 4);
var z = Complex.from(5);
var z = Complex.from('2+5i');

Constant: Complex.i: A instance of the imaginary unit i

var i = Complex.i;

Constant: Complex.one: An instance for the real number 1 var one = Complex.one;

Method: fromRect: Sets the real and imaginary properties a and b from a + bi

myComplex.fromRect(real, im);

Arguments:

1. real (number): the real part of the number
2. im (number): the imaginary part of the number

Method: fromPolar: Sets the a and b in a + bi from a polar representation.

myComplex.fromPolar(r, phi);

Arguments:

1. r (number): the radius/magnitude of the number
2. phi (number): the angle/phase of the number

Method: toPrecision Sets the precision of the numbers. Similar to Number.prototype.toPrecision. Useful before printing the number with the toString

myComplex.toPrecision(k);

Argument:

1. k (number): an integer specifying the number of significant digits

Method: toFixed: Formats a number using fixed-point notation. Similar to Number.prototype.toFixed. Useful before printing the number with the toString

myComplex.toFixed(k);

Argument:

1. k (number): the number of digits to appear after the decimal point; this may be a value between 0 and 20, inclusive, and implementations may optionally support a larger range of values. If this argument is omitted, it is treated as 0

Method: finalize: Finalizes the instance. The number will not change and any other method call will return a new instance. Very useful when a complex instance should stay constant. For example the Complex.i variable is a finalized instance.

myComplex.finalize();

Method: magnitude: Calculates the magnitude of the complex number

myComplex.magnitude(); Alias: • abs

Method: angle: Calculates the angle with respect to the real axis, in radians.

myComplex.angle();

Aliases • arg • phase

Method: conjugate: Calculates the conjugate of the complex number (multiplies the imaginary part with -1)

myComplex.conjugate();

Method: negate: Negates the number (multiplies both the real and imaginary part with -1)

myComplex.negate();

Method: multiply: Multiplies the number with a real or complex number

myComplex.multiply(z);

Arguments:

1. z (number, complex) the number to multiply with

Alias: • mult

Method: divide: Divides the number by a real or complex number

myComplex.divide(z);

Arguments:

1. z (number, complex): the number to divide by Alias: • div

Method: add: Adds a real or complex number

myComplex.add(z);

Arguments:

1. z (number, complex): the number to add

Method: subtract: Subtracts a real or complex number

myComplex.subtract(z);

Arguments:

1. z (number, complex): the number to subtract Alias: • sub

Method: pow: Returns the base to the exponent

myComplex.pow(z);

Arguments:

1. z (number, complex) the exponent

Method: sqrt: Returns the square root

myComplex.sqrt();

Method: log: Returns the natural logarithm (base E)

myComplex.log([k]);

Arguments:

1. k (number): the actual answer has a multiplicity (ln(z) = ln|z| + arg(z)) where arg(z) can return the same for different angles (every 2*pi), with this argument you can define which answer is required

Method: exp: Calculates the e^z where the base is E and the exponential the complex number.

myComplex.exp();

Method: sin: Calculates the sine of the complex number

myComplex.sin();

Method: cos: Calculates the cosine of the complex number

myComplex.cos();

Method: tan: Calculates the tangent of the complex number

myComplex.tan();

Method: sinh: Calculates the hyperbolic sine of the complex number

myComplex.sinh();

Method: cosh: Calculates the hyperbolic cosine of the complex number

myComplex.cosh();

Method: tanh: Calculates the hyperbolic tangent of the complex number

myComplex.tanh();

Method: clone: Returns a new Complex instance with the same real and imaginary properties

myComplex.clone();

Method: toString: Returns a string representation of the complex number

myComplex.toString();

Examples:

new Complex(1, 2).toString(); // 1+2i
new Complex(0, 1).toString(); // i
new Complex(4, 0).toString(); // 4
new Complex(1, 1).toString(); // 1+i

Method: Equals: Checks if the real and imaginary components are equal to the passed in compelex components.

myComplex.equals(z);

Arguments:

1. z (number, complex): the complex number to compare with

Examples:

new Complex(1, 4).equals(new Complex(1, 4)); // true
new Complex(1, 4).equals(new Complex(1, 3)); // false