# Vocabulary/jdot

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`j. y`Imaginary

Rank 0 *-- operates on individual atoms of y, producing a result of the same shape --*
WHY IS THIS IMPORTANT?

Multiplies `y` by `0j1`, which represents the imaginary unit ** i** .

Equivalent to `0j1 * y`

j. 5 NB. y real, resulting in the pure imaginary number 0+5i 0j5 5 * 0j1 0j5 j. 3j4 NB. y complex, result is the product (0+1i)*(3+4i) = 3i+4i^2 = -4+3i _4j3

`x j. y`Complex

Rank 0 0 *-- operates on individual atoms of x and y, producing a result of the same shape --*
WHY IS THIS IMPORTANT?

Combines `x` and `y` into a complex number having `x` as its real part and `y` as its imaginary part

Equivalent to `x + 0j1 * y`

3 j. 4 NB. arguments are separated from verb by spaces (x j. y) 3j4 ^ ^ 3j.4 NB. this is a different number, complex constant (3+0.4*i) 3j0.4 1 j. -:%:2 NB. composing complex number (1+sqrt(2)/2*i) 1j0.707107

### Common uses

1. Work with complex arithmetic.

2. Some primitives use a complex argument as a way of putting two numbers into one atom

NB. (":) Format o.>:i.3 NB. first three multiples of π 3.14159 6.28319 9.42478 (o.>:i.3) ,: (*: o.>:i.3) NB. multiples and their squares 3.14159 6.28319 9.42478 9.8696 39.4784 88.8264 13j9 ": (o.>:i.3) ,: (*: o.>:i.3) NB. x is (w j. d), producing formatted output 3.141592654 6.283185307 9.424777961 NB. with d decimal digits and a field width of w 9.869604401 39.478417604 88.826439610 NB. (#) Copy 2j1 # 2 3 5 7 NB. x is (n j. f), specifying n copies followed by f fills 2 2 0 3 3 0 5 5 0 7 7 0 0 2j1 1 3 # 2 3 5 7 3 3 0 5 7 7 7 NB. (i:) Steps i: 2j3 NB. y is (a j. n), calling for n steps in intervall [-a,a] _2 _0.666667 0.666667 2

3. Handle *x/y* screen coordinates as complex numbers instead of pairs of reals.

j4xy=: _2 j./\ ] NB. a list of xy-coords --> a list of complex nos xy4j=: [: , +. NB. a list of complex nos --> a list of xy-coords j4xy 3 4 _2 3 3j4 _2j3 xy4j 3j4 _2j3 3 4 _2 3

### Related primitives

Real/Imag (`+. y`),
Signum (Unit Circle) (`* y`),
Length/Angle (`*. y`),
Magnitude (`* y`),
Circle Functions (`x o. y`),
Angle * Polar (`r.`)