USER’S MANUAL__________________________________________________________________
182 _________________________________________________________________ M211322EN-D
s = W × Y
is computed as
Real{s} = Real{W} Real{Y} - Imag{W} Imag{Y}
Imag{s} = Real{W} Imag{Y} + Imag{W} Real{Y}
where "Real{}" and "Imag{}" represent the real and imaginary parts of
their complex-valued argument. Note that all of the expanded
computations are themselves real-valued.
In addition to the usual operations of addition, subtraction, division, and
multiplication of complex numbers, we employ three additional unary
operators: "||", "Arg" and "*". Given a number "s" in the complex plane,
the magnitude (or modulus) of s is equal to the length of the vector joining
the origin with "s", that is by Pythagoras:
The signed (CCW positive) angle made between the positive real axis and
the above vector is:
where this angle lies between - π and + π and the signs of Real{s} and Imag
{s} determine the proper quadrant. Note that this angle is real, and is
uniquely defined as long as |s| is non-zero. When |s| is equal to zero, Arg{s}
is undefined. Finally, the "complex conjugate" of "s" is that value obtained
by negating the imaginary part of the number, i.e.,
s* = Real{s} - j Imag{s}.
Note that Arg{s*} = -Arg{s}. The reader is referred to any introductory
text on complex numbers for clarification of these points.
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