Complex Functions

Let i be an imaginary unit.

Let x , y be real numbers, z be a complex

COMPLEX(x , y) | Complex number x + y i
RE(z) | The real part of z, i.e., RE(x + y i)= x
IM(z) | The imaginary part of z, i.e., IM(x + y i)= y
CONJ(z) | The conjugate of z, i.e., CONJ(x + y i)= x - y i
ARG(z) | The argument of z, i.e., arg z . The result depends on the angle option. In case of angle radians, the result is greater than -π and not greater than π. In case of angle degrees, the result is greater than -180° and not greater than 180°,
ABS(z) | The absolute value of z, |z|
SQR(z) | The square root of z, the argument of which is greater than that -π and not greater than π. For example, SQR(-1)=i.
EXP(z) | The exponential function.
LOG(z) | The natural logarithm of z, i.e., the complex number with real part log|z|, imaginary part arg z, where the unit is radians and is greater than π and not greater than π

<Note> EXP(z) and LOG(z) are not affected by the angle option.

Dot product
Let a and b be two 1-dimentional arrays defined as follows.
DIM a(n),b(n)
Then
DOT(a,b) = a(1)*conj(b(1)) + a(2)*conj(b(1)) + … + a(n)*conj(b(n))