+ Conjugate - Plus

>> << Ndx Usr Pri Phr Dic Rel Voc !: wd Help Dictionary

Conjugate | + 0 0 0 | Plus

`+ y` is the conjugate of`y` .`` For example,`+3j4` is`3j_4` . |  | `+` is defined as in elementary arithmetic, and is extended to complex numbers as usual.

A complex number`y` multiplied by its conjugate produces a real number equal to the square of its magnitude`|y` .`` For example:

       3j4 * 3j_4
    25

The function`j.``` multiplies its argument by the square root of negative one:

       ]i=: i. 5
    0 1 2 3 4

       j. i
    0 0j1 0j2 0j3 0j4

       ]y=: i + 2 * j. i
    0 1j2 2j4 3j6 4j8

       +y
    0 1j_2 2j_4 3j_6 4j_8

       y * +y
    0 5 20 45 80

       %: y * +y
    0 2.23607 4.47214 6.7082 8.94427

       |y
    0 2.23607 4.47214 6.7082 8.94427

The conjugate of`y` can also be expressed as`(|y*y)%y` .`` For example:

       (|y*y)%y
    0 1j_2 2j_4 3j_6 4j_8

>> << Ndx Usr Pri Phr Dic Rel Voc !: wd Help Dictionary