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This JavaScript program (by Stephen R. Schmitt) performs the following complex arithmetic operations:

z = x + y add y to x
z = x - y subtract y from x
z = x * y multiply x by y
z = x / y divide x by y
z = 1 / x inverse of x
z = x^2 x squared
z = sqrt x square root of x
z = | x | absolute value of x
z = arg x argument of x in radians
z = exp x base e raised to power x
z = ln x natural logarithm of x
z -> x copy z to x
z -> y copy z to y
x <=> y swap x and y

To operate the calculator, enter the values of complex numbers into x and y and then press the button corresponding to the desired operation.

To reset the input windows, press the 'Clear' button

x = + j

y = + j

z = + j

Notes

A complex number is represented as:

    z = a + jb

where j2 = -1. Letting,

    x = a + jb
    y = c + jd
    r = sqrt (a2 + b2)
    t = arctan( b/a ) 

the operations of the calculator are performed as follows:

    x + y = (a + c) + j(b + d)

    x - y = (a - c) + j(b - d)

    x * y = (ac - bd) + j(ad + bc)

    x / y = [(ac + bd) + j(bc - ad)] / (c2 + d2)

    1 / x = (a - bj) / (a2 + b2)

    x2 = (a2 - b2) + 2abj

    sqrt x = (sqrt r)(sin t/2 + j cos t/2)

    | x | = sqrt (a2 + b2)

    arg x = arctan( b/a )

    exp x = ea(cos b + j sin b) 

    ln x  = ln r + j t 

The calculator computes only the principle value for multivalued functions.

Copyright © 2004, Stephen R. Schmitt