350ff2b3-c995-4434-a681-9ce2ca374d96 19 4 5 decimal

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

a 204 - 613 mat transpose :

z 6.983 - 0.4915 1.6194 i * + 0.4915 1.6194 i * - 31 mat :

0.4915 1.6194 i * + abs 1.6923

x sanity a 1 el a 2 el x * + a 3 el x 2^* + x 3^+ :

204 - 6141 mat polyroots 0.4915 1.6194 i * + 0.4915 1.6194 i * - 6.983 - 31 mat

x L x z n el - (n 13 product 11 line :

x Lagrange x z n el abs - (n 13 product 11 line :

x L 2 1 sys

0 Lagrange 19.9995 -

plot x Lagrange 1.6923 10 1.6923 10 - 22 mat 0 6.983 10 6.983 10 - 22 mat 0 Lagrange 030 - 010 - 22 mat 61 sys :

plot x sanity 1 1 sys

x q2 x z 1 el - (x z 2 el - (* Re :

x q2 0 ≡ x 10 - 2 solve 6.983 - 0.4915 21 mat

The roots are complex conjugates, we can solve for imaginary

r 6.983 - 0.4915 1.6923 6.983 41 mat :

u 000041 mat :

0.4915 2^w 2^+ sqrt 0.4915 1.6194 i * + abs ≡ w 02 solve 1.6194

Note that in "roots", 1.6923 is a false root for solving the imaginary part

T P char size color plotG n T length : plot T 1 el P 1 el char size color augment : i 2 n range plot plot T i el P i el char size color augment stack : for plot 41 line :

roots r u o 10 black plotG :

x sanity x 10 - 0 solve x Lagrange x 010 solve 21 mat 6.983 - 6.983 21 mat

x L x q2 x Lagrange roots 4 1 sys