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Complex Arithmetic Calculator

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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