OSCAT BASIC ComplexMathematics - RWTH-EBC/AixOCAT GitHub Wiki

7. Complex Mathematics

7.1. INTRODUCTION

Complex numbers are shown with the defned type COMPLEX.
The type COMPLEX consists of a real part and an imaginary part, both
components are of type REAL.
The complex number Z of type COMPLEX consists of:
*.RE Real part of type REAL.
*.IM Imaginary part of the type REAL.

7.2. CABS

Type Function: REAL
Input X: COMPLEX (Input)
Output REAL (result)

CABS calculates the length of the vector of a complex number The absolu-
te value is also module or Magnitude mentioned.
CABS = SQRT(X.RE² + X.IM²)

7.3. CaCO

Type Function: COMPLEX
Input X: COMPLEX (Input)
Output COMPLEX (result)

Cacos calculates the arc cosine of a complex number
The range of values of the result is between [0, π] for the real part and [-
∞, +∞] for the imaginary part.

7.4. CACOSH

Type Function: COMPLEX
Input X: COMPLEX (Input)
Output COMPLEX (result)

CACOSH calculates the arc hyperbolic cosine of a complex number
[fzy] The range of values of the result is between [-  ,+  ] For the imagi-
nary part.

7.5. CADD

Type Function: COMPLEX
Input X: COMPLEX (Input)
Y:COMPLEX(Input value)
Output COMPLEX (result)

CADD adds two complex numbers X and Y.

7.6. CARG

Type Function: REAL
Input X: COMPLEX (Input value)

Output REAL (result)

CARG calculates the angle of a complex number in the coordinate system.
The range of values of the result is between [-π , +π ].

7.7. CASIN

Type Function: COMPLEX
Input X: COMPLEX (Input)
Output COMPLEX (result)

CASIN calculates the arc sine of a complex number
The range of values of the result is between [-/2,+/2 ] For the imagina-
ry part.

7.8. CASINH

Type Function: COMPLEX
Input X: COMPLEX (Input)
Output COMPLEX (result)

CASINH calculates the arc hyperbolic sine of a complex number
[fzy] The range of values of the result is between [-  ,+  ] For the imagi-
nary part.

7.9. CATAN

Type Function: COMPLEX
Input X: COMPLEX (Input)
Output COMPLEX (result)

ATAN calculates the arc tangent of a complex number
The range of values of the result is between [-/2,+/2 ] For the imagina-
ry part.

7.10. CATANH

Type Function: COMPLEX
Input X: COMPLEX (Input)
Output COMPLEX (result)

CATANH calculates the arc hyperbolic tangent of a complex number
The range of values of the result is between [- /2,+/2 ] for the imagina-
ry part.

7.11. CCON

Type Function: COMPLEX
Input X: COMPLEX (Input)
Output COMPLEX (result)

CCON calculated the conjugation of a complex number
CCON.RE = X.RE

CCON.IM = -X.IM

7.12. CCOS

Type Function: COMPLEX
Input X: COMPLEX (Input)
Output COMPLEX (result)

CCOs calculates the cosine of a complex number

7.13. CCOSH

Type Function: COMPLEX
Input X: COMPLEX (Input)
Output COMPLEX (result)

CCOSH calculates the hyperbolic cosine of a complex number

7.14. CDIV

Type Function: COMPLEX
Input X: COMPLEX (Input)
Y:COMPLEX(Input value)
Output COMPLEX (result)

CDIV dividing two complex numbers X / Y.

7.15. CEXP

Type Function: COMPLEX
Input X: COMPLEX (Input)
Output COMPLEX (result)

CEXP calculates the complex exponent to base E, CEXP = E^X.

7.16. CINV

Type Function: COMPLEX
Input X: COMPLEX (Input)
Output COMPLEX (result)

CINV calculated the reciprocal of a complex number, CINV = 1/X

7.17. CLOG

Type Function: COMPLEX
Input X: COMPLEX (Input)
Output COMPLEX (result)

CLOG calculates the natural logarithm of a complex number raised to E.
CLOG(X) = LOG(e)(X).

7.18. CMUL

Type Function: COMPLEX
Input X: COMPLEX (Input)
Y:COMPLEX(Input value)
Output COMPLEX (result)

CMUL Multiplies two complex numbers X and Y.

7.19. CPOL

Type Function: COMPLEX
Input L: REAL (Length or Radius)
A: REAL (Angle value)
Output COMPLEX (result)

CPOL produces a complex number in polar form. The input values of L and
A specify the length (radius) and the angle.

7.20. CPOW

Type Function: COMPLEX
Input X: COMPLEX (Input)
Y: COMPLEX (input value of 2)
Output COMPLEX (result)

CPOW calculates the power of two Complex numbers, CPOW = X^Y.

7.21. CSET

Type Function: COMPLEX
Input RE: COMPLEX (Real input)
IM: REAL (Imaginary input)
Output COMPLEX (result)

CSET generated from the two input components RE and IM is a complex
number of type COMPLEX.

7.22. Csin

Type Function: COMPLEX
Input X: COMPLEX (Input)
Output COMPLEX (result)

Csin calculates the sine of a complex number

7.23. CSINH

Type Function: COMPLEX
Input X: COMPLEX (Input)

Output COMPLEX (result)

CSINH calculates the hyperbolic sine of a complex number

7.24. CSQRT

Type Function: REAL
Input X: COMPLEX (Input)
Output REAL (result)

CSQRT calculates the square root of a complex number

7.25. CSUB

Type Function: COMPLEX
Input X: COMPLEX (Input)
Y:COMPLEX(Input value)
Output COMPLEX (result)

CSUB Subtracts two complex numbers, Csub = X - Y.

7.26. CTAN

Type Function: COMPLEX

Input X: COMPLEX (Input)
Output COMPLEX (result)

CTAN calculates the tangent of a complex number

7.27. CTANH

Type Function: COMPLEX
Input X: COMPLEX (Input)
Output COMPLEX (result)

CTANH calculates the hyperbolic tangent of a complex number