<p> plot(data,#,size,#) </p>

21248c8b-55fe-4828-9c1f-566df1889504 27 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

General form x y f y x ln * exp :

1 - 0.25 - f 0.7071 0.7071 i * -

preferred specific (-1)^x x r e x i * π *^:

e x i * π *^x i * π * exp ≡

1/1 Mathcad 11 ... 15 D
doctored for overlord Ω 1 - 4 / r 23 / r 1 r 0.36 r 0.5 r 1.23456789 r 1.23456789 - r 71 mat : 0.707106781186547 0.707106781186548 i * - 0.500000000000001 - 0.866025403784438 i * + 1 - 31015 -^* i * - 0.425779291565072 0.90482705246602 i * + 11015 -^* - i + 0.74054403682714 - 0.672007834418441 i * - 0.74054403682714 - 0.672007834418441 i * + 71 mat

Ω arg vectorize ° 45 - 120180 - 64.8 90 137.7778 - 137.7778 71 mat

coeffs 'i' ≥ -1 U i r i - r 0.5 i * - r i 1.125 * r 51 mat : 0.0432 23.1407 4.8105 0.0292 51 mat

v 0.123456789 :

enable/disable v 1.23456789 :

U i 1 * v * exp i 3 * v * exp i 5 * v * exp i 10 * v * exp i 20 * v * exp i 30 * v * exp i 0.5 * v * exp i 0.25 * v * exp i 0.0125 * v * exp i 0.00125 * v * exp 101 mat :

U 0.9924 0.1231 i * + 0.9322 0.362 i * + 0.8155 0.5788 i * + 0.3299 0.944 i * + 0.7823 - 0.6229 i * + 0.8461 - 0.533 i * - 0.9981 0.0617 i * + 0.9995 0.0309 i * + 1 0.0015 i * + 1 0.0002 i * + 101 mat

U abs vectorize 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 0.999999999999999 1.000000000000000 101 mat

U arg vectorize ° 7.0736 21.2207 35.3678 70.7355 141.4711 147.7934 - 3.5368 1.7684 0.0884 0.0088 101 mat

► Otherwise cis(θ) ... fractional circle via 'xo'

u v N var u v u v u - N / + (range : x xo x1 N var : u 0 xo N var : 31 sys

xo 0.375 : x1 1 : N 40 : r 1 : ρ 1.5 : 15 mat

cis r i 2 * π * x * exp vectorize * : ucis 0.5 i 2 * π * u * exp vectorize * : cis cis Re cis Im augment : ucis ucis Re ucis Im augment : 41 sys

Numeric radius 00 cis 11 el cis 12 el 0032 mat :

∠ cis 11 el i cis 12 el * + arg :

CIS ρ i 2 * π * x * exp * vectorize Conjugate : Ncis CIS Re CIS Im augment (: 21 sys

x y axes x y / - :

Ncis rows 41

cis radius Ncis ucis axes 51 sys

cis radius Ncis ucis axes 5 1 sys

Ncis 1.061 - 1.061 - 1.16 - 0.952 - 1.247 - 0.833 - 1.323 - 0.707 - 1.386 - 0.574 - 1.435 - 0.435 - 1.471 - 0.293 - 1.493 - 0.147 - 1.5 - 4.5 1015 -^* 1.493 - 0.147 1.471 - 0.293 1.435 - 0.435 1.386 - 0.574 132 mat

∠ ° 135

z ln z abs ln i z arg * + :

z 0.5 0.125 i * + :

z ln 0.6628 - 0.245 i * +

z ln arg ° 159.7161

x y f x iy + abs ln y x / atan i * + 2 π * i * + :

x 0.5 : y 0.25 i * : 12 mat

x i y * + abs ln y x / atan i * + 2 π * i * + 1.9356 - 6.2832 i * +

x circle 1 x 2^- sqrt ± :

p 14 / :

λ 13 / - :

x plot x circle 00 p r Re p r Im p r Re 032 mat 00 λ r Re λ r Im λ r Re 032 mat 51 sys :

x plot

p r arg λ r arg 21 mat ° 4560 - 21 mat

x 1 - 1 0.875 - range :

Ω x r vectorize :

Ω 1 - 31015 -^* i * + 0.9239 - 0.3827 i * - 0.7071 - 0.7071 i * - 0.3827 - 0.9239 i * - 11015 -^* - i - 0.3827 0.9239 i * - 0.7071 0.7071 i * - 0.9239 0.3827 i * - 1 0.9239 0.3827 i * + 0.7071 0.7071 i * + 0.3827 0.9239 i * + 11015 -^* - i + 0.3827 - 0.9239 i * + 0.7071 - 0.7071 i * + 0.9239 - 0.3827 i * + 1 - 31015 -^* i * - 171 mat

Ω arg vectorize ° 180 157.5 - 135 - 112.5 - 90 - 67.5 - 45 - 22.5 - 0 22.5 45 67.5 90 112.5 135 157.5 180 - 171 mat

Disambiguate ... sanity check ====================

General form of the 'Power Function X^Y' x y f y x ln * exp :

preferred specific (-1)^x ... within 0 ... 2π circle x r e x i * π *^:

NOT compatible Win 7
index outside table 1 - (0.36^#

0.36 r 0.36 r abs 21 mat 0.4258 0.9048 i * + 121 mat

x 1 - :

y 0.36 :

sanity MCD x (y^0.4258 0.9048 i * +

x (y^abs 1

Equivalent triplets x y f x (y^y r 31 mat 0.4258 0.9048 i * + 0.4258 0.9048 i * + 0.4258 0.9048 i * + 31 mat

Roots of Unity

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

x Clear 1

r 1 :

x circle r 2^x 2^- sqrt ± :

n 12 :

roots x n^1 - 0 ≡ x solve maple :

P roots Re roots Im augment r * :

rootsP P . 14 black plot :

x circle rootsP r 0 + 100 green 1 5 mat 3 1 sys

P 101 - 00101 - 0.866 0.5 0.866 - 0.5 - 0.866 0.5 - 0.866 - 0.5 0.5 0.866 - 0.5 0.866 0.5 - 0.866 0.5 - 0.866 - 122 mat

roots 11 - i i - 0.866 0.5 i * + 0.866 - 0.5 i * - 0.866 0.5 i * - 0.866 - 0.5 i * + 0.5 0.866 i * - 0.5 0.866 i * + 0.5 - 0.866 i * + 0.5 - 0.866 i * - 121 mat

n 12

iπ ... ± iπ/2 1 - ln i ln i - ln 31 mat 3.1416 i * 1.5708 i * 1.5708 i * - 31 mat

Roots of Imaginary

j 18 range :

roots_of_imaginary 1 - j nthroot :

roots_of_imaginary vectorize 1 - i 0.5 0.866 i * + 0.7071 0.7071 i * + 0.809 0.5878 i * + 0.866 0.5 i * + 0.901 0.4339 i * + 0.9239 0.3827 i * + 81 mat

roots_of_imaginary arg vectorize ° 1809060453630 25.7143 22.5 81 mat

===== Unexplained/Unsolved =====

x xo n Clear 1

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

XY 0100 0.1 100 0.2 100 0.3 100 0.4 100 0.5 100 0.6 100 0.7 100 0.8 99.03 0.9 83.62 1 52.49 1.1 27.49 1.2 19.52 1.3 6.61 1.4 3.3 1.5 1.69 1.6 0.89 1.7 0.48 1.8 0.27 1.9 0.16 2 0.09 212 mat :

k 0.609318 : xo 0.405489 : n 7.488356 : 31 mat

x J 99 x xo - (n^1 k / (n^* - :

x xo - (n^1 k / (n^*

x xo - k / (n^

data XY . 12 black plot :

Starts @ xo ,,,wrong maths attributed to 'WIN 7 Starter'

data x J 2 1 sys

Mathcad 11 XP

x j 99 x 4054891000000 / - (1872089250000 /^1304659500000 / / (1872089250000 /^* - :

WIN 7 bug confirmed

x J