## A.5.1 Built-in Functions

The standard mathematical functions are defined for complex numbers in general. Many-valued mathematical functions (for instance asin()) return their principal value.

All available functions are listed in Table A.9. The types of the arguments are written within the parentheses.

A simple example which calculates the sine of a Complex:

```a = sin(4.42 + 5.9 j);          // -> -174.9 - 52.6 j
```

The functions sin(), cos(), tan(), and cot() expect their argument in radians. The functions asin(), acos(), atan(), and acot() deliver a result in radians. The functions abs(), arg(), sign(), sigma(), squ(), sqrt(), cub(), and cbrt() may be called with a Real, Complex, or Quantity respectively. sqrt() and cbrt() calculate the square and the cubic root respectively, and, therefore, expect an argument with a square or cubic unit respectively:

```i1 = sqrt(4 "A*A");             // -> 2 A
i2 = cbrt(8 "A*A*A");           // -> 2 A
```

Another, rather simple example calculates the length of the hypotenuse of a right-angled triangle with its short sides given.

```a = 3 A;
b = 4 A;
c = sqrt(squ(a) + squ(b));      // -> 5 A
```

It is to note that the square root of -1 delivers 1.0 j:

```d = sqrt (-4);                  // -> 0.0 + 2.0 j
```

 Function Description abs(Complex Quantity) absolute value arg(Complex Quantity) argument value sign(Real Quantity) sign sigma(Real Quantity) step function sin(Complex) sine cos(Complex) cosine tan(Complex) tangent cot(Complex) cotangent asin(Complex) inverse sine acos(Complex) inverse cosine atan(Complex) inverse tangent acot(Complex) inverse cotangent sinh(Complex) hyperbolic sine cosh(Complex) hyperbolic cosine tanh(Complex) hyperbolic tangent coth(Complex) hyperbolic cotangent asinh(Complex) inverse hyperbolic sine acosh(Complex) inverse hyperbolic cosine atanh(Complex) inverse hyperbolic tangent acoth(Complex) inverse hyperbolic cotangent exp(Complex) exponential function pow(Complex, Complex) argument 1 to the power of argument 2 pow2(Complex) 2 to the power of the given argument pow10(Complex) 10 to the power of the given argument log(Complex) natural logarithm log2(Complex) logarithm to the base 2 log10(Complex) common logarithm (to the base 10) squ(Complex Quantity) square sqrt(Complex Quantity) square root cub(Complex Quantity) power of three cbrt(Complex Quantity) cubic root

Robert Klima 2003-02-06