| m0=: cnj=: + | Conjugate |
| m1=: mag=: | | Magnitude |
| m2=: %:@(cnj*]) | " |
| m3=: rai=: +. | Real and imaginary parts |
| m4=: maa=: *. | Magnitude and angle |
| m5=: irai=: rai^:_1 | Inverse rai |
| m6=: imaa=: maa^:_1 | Inverse maa |
| m7=: rou=: [:^ 0j2p1&% * i. | Roots of unity |
| m8=: rpg=: rai@rou | Regular polygon |
| d9=: zero=: ] * 10&^@-@[ < | | Zero any real y less than 10^-x in mag |
| m10=: z=:({.,{:*1e_6"_<%~/@:|)&.rai | Zero imaginary if relatively small |
m11=: (1e_10&$:) : (j./"1@((] *
(<:|)) +.)) | Clean y |
The function z may be used to zero any imaginary part that is relatively small compared to the corresponding real part. For example: |
(] ,: z) a=:3+j.10^-2*i. 5
3j1 3j0.01 3j0.0001 3j1e_6 3j1e_8
3j1 3j0.01 3j0.0001 3 3
z a
3j1 3j0.01 3j0.0001 3 3
Complex numbers can be scaled by multiplication by a real number, and shifted and rotated by addition and multiplication by complex numbers. For example: |
]a=: rou 3 Third roots of unity
1 _0.5j0.866025 _0.5j_0.866025
|a Lie on the unit circle
1 1 1
1ad30 Complex of mag 1 and angle of 30 degrees
0.866025j0.5
6&zero@rai&.> (] ; 3j4&+ ; 1ad30&* ; 2ad60&*) a
+---------------------------------------------------+
¦ 1 0¦ 4 4¦ 0.866025 0.5¦ 1 1.73205¦
¦ 0.5 0.866025¦2.5 4.86603¦_0.866025 0.5¦_2 0¦
¦_0.5 0.866025¦2.5 3.13397¦ 0 _1¦ 1 _1.73205¦
+---------------------------------------------------+
Coordinates of Shift by 3,4 Rotate by Rotate by
triangle 30 degrees 60 degrees
|