The ComplexArithmetic.lng Model

Complex arithmetic in LINGO

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LINGO uses only real numbers.
Thus, if you wish to work with complex numbers, you must represent each complex number by a pair of real numbers. If we denote the square root of -1 by i,
we write a complex number Z = XR + i*XI.
For some applications, e.g., electrical, it is useful to use polar coordinates,
(XR + i*XI) = R*( COS( THETA) + i*SIN( THETA))
= R*EXP(i*THETA), (using Euler's Formula),
where R = (XR*XR + XI*XI)^0.5, and THETA = ATAN(XI/XR) =
angle in radians whose tangent is XI/XR.
Below are code fragments for how to compute the real and imaginary parts resulting from various math operators;


Complex Number | Imaginary Number |