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6.10.6 Complex Number Operations

@@ A lot of details missing here

• binary operators `+`, `-`, `*`, `/` and unary `-`, `+`
• exponentiation operators (`pow` and `**`)
• functions (`Sqr`, `SqRt`, `Exp`, `Ln`, `Sin`, `Cos`, `ArcSin`, `ArcCos`, `ArcTan`)
• number info with `Re`, `Im` and `Arg` functions
• numbers constructed by `Cmplx` or `Polar`

The following sample programs illustrates most of the `Complex` type operations.

```     program ComplexOperationsDemo (Output);

var
z1, z2: Complex;
Len, Angle: Real;

begin
z1 := Cmplx (2, 1);
WriteLn;
WriteLn ('Complex number z1 is: (', Re (z1) : 1, ',', Im (z1) : 1, ')');
WriteLn;
z2 := Conjugate(z1); { GPC extension }
WriteLn ('Conjugate of z1 is: (', Re (z2) : 1, ',', Im (z2) : 1, ')');
WriteLn;
Len   := Abs (z1);
Angle := Arg (z1);
WriteLn ('The polar representation of z1 is: Length=', Len : 1,
', Angle=', Angle : 1);
WriteLn;
z2 := Polar (Len, Angle);
WriteLn ('Converting (Length, Angle) back to (x, y) gives: (',
Re (z2) : 1, ',', Im (z2) : 1, ')');
WriteLn;
WriteLn ('The following operations operate on the complex number z1');
WriteLn;
z2 := ArcTan (z1);
WriteLn ('ArcTan (z1) = (', Re (z2), ', ', Im (z2), ')');
WriteLn;
z2 := z1 ** 3.141;
WriteLn ('z1 ** 3.141 =', Re (z2), ', ', Im (z2), ')');
WriteLn;
z2 := Sin (z1);
WriteLn ('Sin (z1) = (', Re (z2), ', ', Im (z2), ')');
WriteLn ('(Cos, Ln, Exp, SqRt and Sqr exist also.)');
WriteLn;
z2 := z1 pow 8;
WriteLn ('z1 pow 8 = (', Re (z2), ', ', Im (z2), ')');
WriteLn;
z2 := z1 pow (-8);
WriteLn ('z1 pow (-8) = (', Re (z2), ', ', Im (z2), ')');
end.
```