complex
Do calculations with Complex numbers
npm install complex
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Version | 3.0.1 last updated 3 months ago |
License | MIT |
Keywords | Complex Numbers, Numbers, Math, Calculus |
Repository | http://github.com/arian/Complex (git) |
Homepage | http://github.com/arian/Complex |
Bugs | https://github.com/arian/Complex/issues |
Dependencies | None |
Complex
Complex is a additional Type to deal with Complex Numbers in JavaScript. It provides several methods to add, multiply numbers as well as calculate the magnitude and angle in the complex plane.
Node
You can get this package with NPM:
npm install Complex
var Complex = require('Complex');
console.log(new Complex(3, 4).abs()); // 5
Browser
Complex can be built for the browser with wrapup or other tools that can generate browser JS from Node packages.
Testing
Testing is done with Mocha and Expect.js:
# install dependencies
npm install
# run the tests in node
./node_modules/.bin/mocha test/Complex.js
or testing in the browser:
# install dependencies
npm install
# run a small node server
node ./test/server.js
# run tests
google-chrome http://localhost:3000
API Documentation
Complex constructor:
var z = new Complex(real im);
Arguments:
- real (number) the real part of the number
- im (number) the imaginary part of the number
Function: Complex.from
A in line function like Number.from.
var z = Complex.from(real[, im]);
Arguments:
- real (number) the real part of the number
- im (number, optional) the imaginary part of the number
Or
- 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');
Function: Complex.fromPolar
Creates a complex instance from a polar representation: r*e^(phi*i) = r (cos(phi) + i sin(phi))
var z = Complex.fromPolar(r, phi);
Arguments:
- r (number) the radius/magnitude of the number
- phi (number) the angle/phase of the number
Constant: Complex.i
A instance of the imaginary unit i
var i = Complex.i;
Constant: Complex.one
A 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:
- real (number) the real part of the number
- 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:
- r (number) the radius/magnitude of the number
- phi (number) the angle/phase of the number
Method: toPrecision
Sets the precision of the numbers. Similar to Number.prototype.toPrecision. Useful befor printing the number with the toString method.
myComplex.toPrecision(k);
Arguments:
- 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 method.
myComplex.toFixed(k);
Arguments:
- 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:
- 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:
- z (number, complex) the number to divide by
Alias:
- div
Method: add
Adds a real or complex number
myComplex.add(z);
Arguments:
- z (number, complex) the number to add
Method: subtract
Subtracts a real or complex number
myComplex.subtract(z);
Arguments:
- z (number, complex) the number to subtract
Alias:
- sub
Method: pow
Returns the base to the exponent
myComplex.pow(z);
Arguments:
- 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:
- 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
'my Complex Number is: ' + (new Complex(3, 5)); // 'my Complex Number is: 3+5i
Method: Equals
Checks if the real and imaginary components are equal to the passed in compelex components.
myComplex.equals(z);
Arguments:
- 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
MIT License
Copyright (c) 2014 Arian Stolwijk
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.