The Identity/Plus Function +

Monadic Use On Floats And Integers

+ is a monadic function that for a complex number returns the complex conjugate of the argument, otherwise it is an identity function.

+ 0 1 2 ¯1 2.0 3e+1

0 1 2 ¯1 2.0 30.0

Dyadic Use On Floats And Integers

+ is a dyadic function that works in two ways.

If the rho of both sides is the same it performs zip-wise addition

If either side has a rho of [1] it adds the value to every value in the other.

Here are some examples:

1 2 3.0 + 3 4 5

4 6 8.0

and

1 2 3 4 5 + 33

34 35 36 37 38

and

1 + 22 33 44 55

23 34 45 56

Monadic Use On Complex Nos

the + function returns the complex conjugate of a complex no.

The complex conjugate of a complex number is the complex number which when multiplied by the original gives a real number.

This is done by flipping the sign of the imaginary component.

+ 1J2 1J¯2 1.0J2.0 1.0j¯2.0

1J¯2 1J2 1.0J¯2.0 1.0J2.0

Dyadic Use On Complex Nos

This is normal complex addition - the real parts are summed and the imaginary:

1J2 3J¯3 + 4j¯5 ¯1j4

5J¯3 2J1

Dyadic Mixed Use On Complex Nos And Real Numbers

In mixed use the real numbers are cast to a complex number with an imaginary value of zero:

1 3J4 + 3J4 1

4J4 4J4