2(xy+y)y+x(y^4+1)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
/ / / _________\ / _________\ \\ / / / _________\ / _________\ \\
____________________________________________________________________________________ | | |\/ 1 + 2*x | im(x) |\/ 1 + 2*x | re(x) || ____________________________________________________________________________________ | | |\/ 1 + 2*x | im(x) |\/ 1 + 2*x | re(x) ||
/ 2 2 |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------|| / 2 2 |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||
/ / / _________\ \ / / _________\ \ | | \ x / 2 2 \ x / 2 2 || / / / _________\ \ / / _________\ \ | | \ x / 2 2 \ x / 2 2 ||
/ | |\/ 1 + 2*x | im(x) | | |\/ 1 + 2*x | re(x) | | \ im (x) + re (x) im (x) + re (x)/| / | |\/ 1 + 2*x | im(x) | | |\/ 1 + 2*x | re(x) | | \ im (x) + re (x) im (x) + re (x)/|
y1 = - / |- im|-----------| + ---------------| + |-1 - re|-----------| - ---------------| *cos|----------------------------------------------------------------------------------| - I* / |- im|-----------| + ---------------| + |-1 - re|-----------| - ---------------| *sin|----------------------------------------------------------------------------------|
4 / | \ x / 2 2 | | \ x / 2 2 | \ 2 / 4 / | \ x / 2 2 | | \ x / 2 2 | \ 2 /
\/ \ im (x) + re (x)/ \ im (x) + re (x)/ \/ \ im (x) + re (x)/ \ im (x) + re (x)/
y1=−i4(−im(x2x+1)+(re(x))2+(im(x))2im(x))2+(−re(x2x+1)−1−(re(x))2+(im(x))2re(x))2sin2atan2(−im(x2x+1)+(re(x))2+(im(x))2im(x),−re(x2x+1)−1−(re(x))2+(im(x))2re(x))−4(−im(x2x+1)+(re(x))2+(im(x))2im(x))2+(−re(x2x+1)−1−(re(x))2+(im(x))2re(x))2cos2atan2(−im(x2x+1)+(re(x))2+(im(x))2im(x),−re(x2x+1)−1−(re(x))2+(im(x))2re(x))
/ / / _________\ / _________\ \\ / / / _________\ / _________\ \\
____________________________________________________________________________________ | | |\/ 1 + 2*x | im(x) |\/ 1 + 2*x | re(x) || ____________________________________________________________________________________ | | |\/ 1 + 2*x | im(x) |\/ 1 + 2*x | re(x) ||
/ 2 2 |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------|| / 2 2 |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||
/ / / _________\ \ / / _________\ \ | | \ x / 2 2 \ x / 2 2 || / / / _________\ \ / / _________\ \ | | \ x / 2 2 \ x / 2 2 ||
/ | |\/ 1 + 2*x | im(x) | | |\/ 1 + 2*x | re(x) | | \ im (x) + re (x) im (x) + re (x)/| / | |\/ 1 + 2*x | im(x) | | |\/ 1 + 2*x | re(x) | | \ im (x) + re (x) im (x) + re (x)/|
y2 = / |- im|-----------| + ---------------| + |-1 - re|-----------| - ---------------| *cos|----------------------------------------------------------------------------------| + I* / |- im|-----------| + ---------------| + |-1 - re|-----------| - ---------------| *sin|----------------------------------------------------------------------------------|
4 / | \ x / 2 2 | | \ x / 2 2 | \ 2 / 4 / | \ x / 2 2 | | \ x / 2 2 | \ 2 /
\/ \ im (x) + re (x)/ \ im (x) + re (x)/ \/ \ im (x) + re (x)/ \ im (x) + re (x)/
y2=i4(−im(x2x+1)+(re(x))2+(im(x))2im(x))2+(−re(x2x+1)−1−(re(x))2+(im(x))2re(x))2sin2atan2(−im(x2x+1)+(re(x))2+(im(x))2im(x),−re(x2x+1)−1−(re(x))2+(im(x))2re(x))+4(−im(x2x+1)+(re(x))2+(im(x))2im(x))2+(−re(x2x+1)−1−(re(x))2+(im(x))2re(x))2cos2atan2(−im(x2x+1)+(re(x))2+(im(x))2im(x),−re(x2x+1)−1−(re(x))2+(im(x))2re(x))
/ / / _________\ / _________\\\ / / / _________\ / _________\\\
__________________________________________________________________________________ | | im(x) |\/ 1 + 2*x | re(x) |\/ 1 + 2*x ||| __________________________________________________________________________________ | | im(x) |\/ 1 + 2*x | re(x) |\/ 1 + 2*x |||
/ 2 2 |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------||| / 2 2 |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------|||
/ / / _________\\ / / _________\\ | | 2 2 \ x / 2 2 \ x /|| / / / _________\\ / / _________\\ | | 2 2 \ x / 2 2 \ x /||
/ | im(x) |\/ 1 + 2*x || | re(x) |\/ 1 + 2*x || | \im (x) + re (x) im (x) + re (x) /| / | im(x) |\/ 1 + 2*x || | re(x) |\/ 1 + 2*x || | \im (x) + re (x) im (x) + re (x) /|
y3 = - / |--------------- + im|-----------|| + |-1 - --------------- + re|-----------|| *cos|--------------------------------------------------------------------------------| - I* / |--------------- + im|-----------|| + |-1 - --------------- + re|-----------|| *sin|--------------------------------------------------------------------------------|
4 / | 2 2 \ x /| | 2 2 \ x /| \ 2 / 4 / | 2 2 \ x /| | 2 2 \ x /| \ 2 /
\/ \im (x) + re (x) / \ im (x) + re (x) / \/ \im (x) + re (x) / \ im (x) + re (x) /
y3=−i4(im(x2x+1)+(re(x))2+(im(x))2im(x))2+(re(x2x+1)−1−(re(x))2+(im(x))2re(x))2sin2atan2(im(x2x+1)+(re(x))2+(im(x))2im(x),re(x2x+1)−1−(re(x))2+(im(x))2re(x))−4(im(x2x+1)+(re(x))2+(im(x))2im(x))2+(re(x2x+1)−1−(re(x))2+(im(x))2re(x))2cos2atan2(im(x2x+1)+(re(x))2+(im(x))2im(x),re(x2x+1)−1−(re(x))2+(im(x))2re(x))
/ / / _________\ / _________\\\ / / / _________\ / _________\\\
__________________________________________________________________________________ | | im(x) |\/ 1 + 2*x | re(x) |\/ 1 + 2*x ||| __________________________________________________________________________________ | | im(x) |\/ 1 + 2*x | re(x) |\/ 1 + 2*x |||
/ 2 2 |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------||| / 2 2 |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------|||
/ / / _________\\ / / _________\\ | | 2 2 \ x / 2 2 \ x /|| / / / _________\\ / / _________\\ | | 2 2 \ x / 2 2 \ x /||
/ | im(x) |\/ 1 + 2*x || | re(x) |\/ 1 + 2*x || | \im (x) + re (x) im (x) + re (x) /| / | im(x) |\/ 1 + 2*x || | re(x) |\/ 1 + 2*x || | \im (x) + re (x) im (x) + re (x) /|
y4 = / |--------------- + im|-----------|| + |-1 - --------------- + re|-----------|| *cos|--------------------------------------------------------------------------------| + I* / |--------------- + im|-----------|| + |-1 - --------------- + re|-----------|| *sin|--------------------------------------------------------------------------------|
4 / | 2 2 \ x /| | 2 2 \ x /| \ 2 / 4 / | 2 2 \ x /| | 2 2 \ x /| \ 2 /
\/ \im (x) + re (x) / \ im (x) + re (x) / \/ \im (x) + re (x) / \ im (x) + re (x) /
y4=i4(im(x2x+1)+(re(x))2+(im(x))2im(x))2+(re(x2x+1)−1−(re(x))2+(im(x))2re(x))2sin2atan2(im(x2x+1)+(re(x))2+(im(x))2im(x),re(x2x+1)−1−(re(x))2+(im(x))2re(x))+4(im(x2x+1)+(re(x))2+(im(x))2im(x))2+(re(x2x+1)−1−(re(x))2+(im(x))2re(x))2cos2atan2(im(x2x+1)+(re(x))2+(im(x))2im(x),re(x2x+1)−1−(re(x))2+(im(x))2re(x))
y4 = i*((im(sqrt(2*x + 1)/x) + im(x)/(re(x)^2 + im(x)^2))^2 + (re(sqrt(2*x + 1)/x) - 1 - re(x)/(re(x)^2 + im(x)^2))^2)^(1/4)*sin(atan2(im(sqrt(2*x + 1)/x) + im(x)/(re(x)^2 + im(x)^2, re(sqrt(2*x + 1)/x) - 1 - re(x)/(re(x)^2 + im(x)^2))/2) + ((im(sqrt(2*x + 1)/x) + im(x)/(re(x)^2 + im(x)^2))^2 + (re(sqrt(2*x + 1)/x) - 1 - re(x)/(re(x)^2 + im(x)^2))^2)^(1/4)*cos(atan2(im(sqrt(2*x + 1)/x) + im(x)/(re(x)^2 + im(x)^2), re(sqrt(2*x + 1)/x) - 1 - re(x)/(re(x)^2 + im(x)^2))/2))
Suma y producto de raíces
[src]
/ / / _________\ / _________\ \\ / / / _________\ / _________\ \\ / / / _________\ / _________\ \\ / / / _________\ / _________\ \\ / / / _________\ / _________\\\ / / / _________\ / _________\\\ / / / _________\ / _________\\\ / / / _________\ / _________\\\
____________________________________________________________________________________ | | |\/ 1 + 2*x | im(x) |\/ 1 + 2*x | re(x) || ____________________________________________________________________________________ | | |\/ 1 + 2*x | im(x) |\/ 1 + 2*x | re(x) || ____________________________________________________________________________________ | | |\/ 1 + 2*x | im(x) |\/ 1 + 2*x | re(x) || ____________________________________________________________________________________ | | |\/ 1 + 2*x | im(x) |\/ 1 + 2*x | re(x) || __________________________________________________________________________________ | | im(x) |\/ 1 + 2*x | re(x) |\/ 1 + 2*x ||| __________________________________________________________________________________ | | im(x) |\/ 1 + 2*x | re(x) |\/ 1 + 2*x ||| __________________________________________________________________________________ | | im(x) |\/ 1 + 2*x | re(x) |\/ 1 + 2*x ||| __________________________________________________________________________________ | | im(x) |\/ 1 + 2*x | re(x) |\/ 1 + 2*x |||
/ 2 2 |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------|| / 2 2 |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------|| / 2 2 |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------|| / 2 2 |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------|| / 2 2 |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------||| / 2 2 |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------||| / 2 2 |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------||| / 2 2 |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------|||
/ / / _________\ \ / / _________\ \ | | \ x / 2 2 \ x / 2 2 || / / / _________\ \ / / _________\ \ | | \ x / 2 2 \ x / 2 2 || / / / _________\ \ / / _________\ \ | | \ x / 2 2 \ x / 2 2 || / / / _________\ \ / / _________\ \ | | \ x / 2 2 \ x / 2 2 || / / / _________\\ / / _________\\ | | 2 2 \ x / 2 2 \ x /|| / / / _________\\ / / _________\\ | | 2 2 \ x / 2 2 \ x /|| / / / _________\\ / / _________\\ | | 2 2 \ x / 2 2 \ x /|| / / / _________\\ / / _________\\ | | 2 2 \ x / 2 2 \ x /||
/ | |\/ 1 + 2*x | im(x) | | |\/ 1 + 2*x | re(x) | | \ im (x) + re (x) im (x) + re (x)/| / | |\/ 1 + 2*x | im(x) | | |\/ 1 + 2*x | re(x) | | \ im (x) + re (x) im (x) + re (x)/| / | |\/ 1 + 2*x | im(x) | | |\/ 1 + 2*x | re(x) | | \ im (x) + re (x) im (x) + re (x)/| / | |\/ 1 + 2*x | im(x) | | |\/ 1 + 2*x | re(x) | | \ im (x) + re (x) im (x) + re (x)/| / | im(x) |\/ 1 + 2*x || | re(x) |\/ 1 + 2*x || | \im (x) + re (x) im (x) + re (x) /| / | im(x) |\/ 1 + 2*x || | re(x) |\/ 1 + 2*x || | \im (x) + re (x) im (x) + re (x) /| / | im(x) |\/ 1 + 2*x || | re(x) |\/ 1 + 2*x || | \im (x) + re (x) im (x) + re (x) /| / | im(x) |\/ 1 + 2*x || | re(x) |\/ 1 + 2*x || | \im (x) + re (x) im (x) + re (x) /|
- / |- im|-----------| + ---------------| + |-1 - re|-----------| - ---------------| *cos|----------------------------------------------------------------------------------| - I* / |- im|-----------| + ---------------| + |-1 - re|-----------| - ---------------| *sin|----------------------------------------------------------------------------------| + / |- im|-----------| + ---------------| + |-1 - re|-----------| - ---------------| *cos|----------------------------------------------------------------------------------| + I* / |- im|-----------| + ---------------| + |-1 - re|-----------| - ---------------| *sin|----------------------------------------------------------------------------------| + - / |--------------- + im|-----------|| + |-1 - --------------- + re|-----------|| *cos|--------------------------------------------------------------------------------| - I* / |--------------- + im|-----------|| + |-1 - --------------- + re|-----------|| *sin|--------------------------------------------------------------------------------| + / |--------------- + im|-----------|| + |-1 - --------------- + re|-----------|| *cos|--------------------------------------------------------------------------------| + I* / |--------------- + im|-----------|| + |-1 - --------------- + re|-----------|| *sin|--------------------------------------------------------------------------------|
4 / | \ x / 2 2 | | \ x / 2 2 | \ 2 / 4 / | \ x / 2 2 | | \ x / 2 2 | \ 2 / 4 / | \ x / 2 2 | | \ x / 2 2 | \ 2 / 4 / | \ x / 2 2 | | \ x / 2 2 | \ 2 / 4 / | 2 2 \ x /| | 2 2 \ x /| \ 2 / 4 / | 2 2 \ x /| | 2 2 \ x /| \ 2 / 4 / | 2 2 \ x /| | 2 2 \ x /| \ 2 / 4 / | 2 2 \ x /| | 2 2 \ x /| \ 2 /
\/ \ im (x) + re (x)/ \ im (x) + re (x)/ \/ \ im (x) + re (x)/ \ im (x) + re (x)/ \/ \ im (x) + re (x)/ \ im (x) + re (x)/ \/ \ im (x) + re (x)/ \ im (x) + re (x)/ \/ \im (x) + re (x) / \ im (x) + re (x) / \/ \im (x) + re (x) / \ im (x) + re (x) / \/ \im (x) + re (x) / \ im (x) + re (x) / \/ \im (x) + re (x) / \ im (x) + re (x) /
i4(im(x2x+1)+(re(x))2+(im(x))2im(x))2+(re(x2x+1)−1−(re(x))2+(im(x))2re(x))2sin2atan2(im(x2x+1)+(re(x))2+(im(x))2im(x),re(x2x+1)−1−(re(x))2+(im(x))2re(x))+4(im(x2x+1)+(re(x))2+(im(x))2im(x))2+(re(x2x+1)−1−(re(x))2+(im(x))2re(x))2cos2atan2(im(x2x+1)+(re(x))2+(im(x))2im(x),re(x2x+1)−1−(re(x))2+(im(x))2re(x))+−i4(im(x2x+1)+(re(x))2+(im(x))2im(x))2+(re(x2x+1)−1−(re(x))2+(im(x))2re(x))2sin2atan2(im(x2x+1)+(re(x))2+(im(x))2im(x),re(x2x+1)−1−(re(x))2+(im(x))2re(x))−4(im(x2x+1)+(re(x))2+(im(x))2im(x))2+(re(x2x+1)−1−(re(x))2+(im(x))2re(x))2cos2atan2(im(x2x+1)+(re(x))2+(im(x))2im(x),re(x2x+1)−1−(re(x))2+(im(x))2re(x))+−i4(−im(x2x+1)+(re(x))2+(im(x))2im(x))2+(−re(x2x+1)−1−(re(x))2+(im(x))2re(x))2sin2atan2(−im(x2x+1)+(re(x))2+(im(x))2im(x),−re(x2x+1)−1−(re(x))2+(im(x))2re(x))−4(−im(x2x+1)+(re(x))2+(im(x))2im(x))2+(−re(x2x+1)−1−(re(x))2+(im(x))2re(x))2cos2atan2(−im(x2x+1)+(re(x))2+(im(x))2im(x),−re(x2x+1)−1−(re(x))2+(im(x))2re(x))+i4(−im(x2x+1)+(re(x))2+(im(x))2im(x))2+(−re(x2x+1)−1−(re(x))2+(im(x))2re(x))2sin2atan2(−im(x2x+1)+(re(x))2+(im(x))2im(x),−re(x2x+1)−1−(re(x))2+(im(x))2re(x))+4(−im(x2x+1)+(re(x))2+(im(x))2im(x))2+(−re(x2x+1)−1−(re(x))2+(im(x))2re(x))2cos2atan2(−im(x2x+1)+(re(x))2+(im(x))2im(x),−re(x2x+1)−1−(re(x))2+(im(x))2re(x))
/ / / / _________\ / _________\ \\ / / / _________\ / _________\ \\\ / / / / _________\ / _________\ \\ / / / _________\ / _________\ \\\ / / / / _________\ / _________\\\ / / / _________\ / _________\\\\ / / / / _________\ / _________\\\ / / / _________\ / _________\\\\
| ____________________________________________________________________________________ | | |\/ 1 + 2*x | im(x) |\/ 1 + 2*x | re(x) || ____________________________________________________________________________________ | | |\/ 1 + 2*x | im(x) |\/ 1 + 2*x | re(x) ||| | ____________________________________________________________________________________ | | |\/ 1 + 2*x | im(x) |\/ 1 + 2*x | re(x) || ____________________________________________________________________________________ | | |\/ 1 + 2*x | im(x) |\/ 1 + 2*x | re(x) ||| | __________________________________________________________________________________ | | im(x) |\/ 1 + 2*x | re(x) |\/ 1 + 2*x ||| __________________________________________________________________________________ | | im(x) |\/ 1 + 2*x | re(x) |\/ 1 + 2*x |||| | __________________________________________________________________________________ | | im(x) |\/ 1 + 2*x | re(x) |\/ 1 + 2*x ||| __________________________________________________________________________________ | | im(x) |\/ 1 + 2*x | re(x) |\/ 1 + 2*x ||||
| / 2 2 |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------|| / 2 2 |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||| | / 2 2 |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------|| / 2 2 |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||| | / 2 2 |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------||| / 2 2 |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------|||| | / 2 2 |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------||| / 2 2 |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------||||
| / / / _________\ \ / / _________\ \ | | \ x / 2 2 \ x / 2 2 || / / / _________\ \ / / _________\ \ | | \ x / 2 2 \ x / 2 2 ||| | / / / _________\ \ / / _________\ \ | | \ x / 2 2 \ x / 2 2 || / / / _________\ \ / / _________\ \ | | \ x / 2 2 \ x / 2 2 ||| | / / / _________\\ / / _________\\ | | 2 2 \ x / 2 2 \ x /|| / / / _________\\ / / _________\\ | | 2 2 \ x / 2 2 \ x /||| | / / / _________\\ / / _________\\ | | 2 2 \ x / 2 2 \ x /|| / / / _________\\ / / _________\\ | | 2 2 \ x / 2 2 \ x /|||
| / | |\/ 1 + 2*x | im(x) | | |\/ 1 + 2*x | re(x) | | \ im (x) + re (x) im (x) + re (x)/| / | |\/ 1 + 2*x | im(x) | | |\/ 1 + 2*x | re(x) | | \ im (x) + re (x) im (x) + re (x)/|| | / | |\/ 1 + 2*x | im(x) | | |\/ 1 + 2*x | re(x) | | \ im (x) + re (x) im (x) + re (x)/| / | |\/ 1 + 2*x | im(x) | | |\/ 1 + 2*x | re(x) | | \ im (x) + re (x) im (x) + re (x)/|| | / | im(x) |\/ 1 + 2*x || | re(x) |\/ 1 + 2*x || | \im (x) + re (x) im (x) + re (x) /| / | im(x) |\/ 1 + 2*x || | re(x) |\/ 1 + 2*x || | \im (x) + re (x) im (x) + re (x) /|| | / | im(x) |\/ 1 + 2*x || | re(x) |\/ 1 + 2*x || | \im (x) + re (x) im (x) + re (x) /| / | im(x) |\/ 1 + 2*x || | re(x) |\/ 1 + 2*x || | \im (x) + re (x) im (x) + re (x) /||
|- / |- im|-----------| + ---------------| + |-1 - re|-----------| - ---------------| *cos|----------------------------------------------------------------------------------| - I* / |- im|-----------| + ---------------| + |-1 - re|-----------| - ---------------| *sin|----------------------------------------------------------------------------------||*| / |- im|-----------| + ---------------| + |-1 - re|-----------| - ---------------| *cos|----------------------------------------------------------------------------------| + I* / |- im|-----------| + ---------------| + |-1 - re|-----------| - ---------------| *sin|----------------------------------------------------------------------------------||*|- / |--------------- + im|-----------|| + |-1 - --------------- + re|-----------|| *cos|--------------------------------------------------------------------------------| - I* / |--------------- + im|-----------|| + |-1 - --------------- + re|-----------|| *sin|--------------------------------------------------------------------------------||*| / |--------------- + im|-----------|| + |-1 - --------------- + re|-----------|| *cos|--------------------------------------------------------------------------------| + I* / |--------------- + im|-----------|| + |-1 - --------------- + re|-----------|| *sin|--------------------------------------------------------------------------------||
| 4 / | \ x / 2 2 | | \ x / 2 2 | \ 2 / 4 / | \ x / 2 2 | | \ x / 2 2 | \ 2 /| |4 / | \ x / 2 2 | | \ x / 2 2 | \ 2 / 4 / | \ x / 2 2 | | \ x / 2 2 | \ 2 /| | 4 / | 2 2 \ x /| | 2 2 \ x /| \ 2 / 4 / | 2 2 \ x /| | 2 2 \ x /| \ 2 /| |4 / | 2 2 \ x /| | 2 2 \ x /| \ 2 / 4 / | 2 2 \ x /| | 2 2 \ x /| \ 2 /|
\ \/ \ im (x) + re (x)/ \ im (x) + re (x)/ \/ \ im (x) + re (x)/ \ im (x) + re (x)/ / \\/ \ im (x) + re (x)/ \ im (x) + re (x)/ \/ \ im (x) + re (x)/ \ im (x) + re (x)/ / \ \/ \im (x) + re (x) / \ im (x) + re (x) / \/ \im (x) + re (x) / \ im (x) + re (x) / / \\/ \im (x) + re (x) / \ im (x) + re (x) / \/ \im (x) + re (x) / \ im (x) + re (x) / /
−i4(−im(x2x+1)+(re(x))2+(im(x))2im(x))2+(−re(x2x+1)−1−(re(x))2+(im(x))2re(x))2sin2atan2(−im(x2x+1)+(re(x))2+(im(x))2im(x),−re(x2x+1)−1−(re(x))2+(im(x))2re(x))−4(−im(x2x+1)+(re(x))2+(im(x))2im(x))2+(−re(x2x+1)−1−(re(x))2+(im(x))2re(x))2cos2atan2(−im(x2x+1)+(re(x))2+(im(x))2im(x),−re(x2x+1)−1−(re(x))2+(im(x))2re(x))i4(−im(x2x+1)+(re(x))2+(im(x))2im(x))2+(−re(x2x+1)−1−(re(x))2+(im(x))2re(x))2sin2atan2(−im(x2x+1)+(re(x))2+(im(x))2im(x),−re(x2x+1)−1−(re(x))2+(im(x))2re(x))+4(−im(x2x+1)+(re(x))2+(im(x))2im(x))2+(−re(x2x+1)−1−(re(x))2+(im(x))2re(x))2cos2atan2(−im(x2x+1)+(re(x))2+(im(x))2im(x),−re(x2x+1)−1−(re(x))2+(im(x))2re(x))−i4(im(x2x+1)+(re(x))2+(im(x))2im(x))2+(re(x2x+1)−1−(re(x))2+(im(x))2re(x))2sin2atan2(im(x2x+1)+(re(x))2+(im(x))2im(x),re(x2x+1)−1−(re(x))2+(im(x))2re(x))−4(im(x2x+1)+(re(x))2+(im(x))2im(x))2+(re(x2x+1)−1−(re(x))2+(im(x))2re(x))2cos2atan2(im(x2x+1)+(re(x))2+(im(x))2im(x),re(x2x+1)−1−(re(x))2+(im(x))2re(x))i4(im(x2x+1)+(re(x))2+(im(x))2im(x))2+(re(x2x+1)−1−(re(x))2+(im(x))2re(x))2sin2atan2(im(x2x+1)+(re(x))2+(im(x))2im(x),re(x2x+1)−1−(re(x))2+(im(x))2re(x))+4(im(x2x+1)+(re(x))2+(im(x))2im(x))2+(re(x2x+1)−1−(re(x))2+(im(x))2re(x))2cos2atan2(im(x2x+1)+(re(x))2+(im(x))2im(x),re(x2x+1)−1−(re(x))2+(im(x))2re(x))
/ / _________\ / / _________\\ \ / / _________\ / / _________\\ \
|/ 2 2 \ |\/ 1 + 2*x | | |\/ 1 + 2*x || / 2 2 \| | / 2 2 \ |\/ 1 + 2*x | | |\/ 1 + 2*x || / 2 2 \|
|\im (x) + re (x)/*im|-----------| + im(x) -re(x) + |-1 + re|-----------||*\im (x) + re (x)/| |- \im (x) + re (x)/*im|-----------| + im(x) -re(x) - |1 + re|-----------||*\im (x) + re (x)/|
____________________________________________________________________________________________________ ___________________________________________________________________________________________________ | \ x / \ \ x // | | \ x / \ \ x // |
/ 2 2 / 2 2 I*atan2|-----------------------------------------, -------------------------------------------------| + I*atan2|-------------------------------------------, ------------------------------------------------|
/ / / _________\\ // / _________\\ \ / // / _________\\ \ / / _________\ \ | 2 2 2 2 | | 2 2 2 2 |
/ | / 2 2 \ |\/ 1 + 2*x || || |\/ 1 + 2*x || / 2 2 \ | / || |\/ 1 + 2*x || / 2 2 \ | |/ 2 2 \ |\/ 1 + 2*x | | \ im (x) + re (x) im (x) + re (x) / \ im (x) + re (x) im (x) + re (x) /
/ |-im(x) + \im (x) + re (x)/*im|-----------|| + ||1 + re|-----------||*\im (x) + re (x)/ + re(x)| * / ||1 - re|-----------||*\im (x) + re (x)/ + re(x)| + |\im (x) + re (x)/*im|-----------| + im(x)| *e
\/ \ \ x // \\ \ x // / \/ \\ \ x // / \ \ x / /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ 2 2 \
\im (x) + re (x)/
((re(x))2+(im(x))2)2((1−re(x2x+1))((re(x))2+(im(x))2)+re(x))2+(((re(x))2+(im(x))2)im(x2x+1)+im(x))2(((re(x))2+(im(x))2)(re(x2x+1)+1)+re(x))2+(((re(x))2+(im(x))2)im(x2x+1)−im(x))2eiatan2((re(x))2+(im(x))2−((re(x))2+(im(x))2)im(x2x+1)+im(x),(re(x))2+(im(x))2−((re(x))2+(im(x))2)(re(x2x+1)+1)−re(x))+iatan2((re(x))2+(im(x))2((re(x))2+(im(x))2)im(x2x+1)+im(x),(re(x))2+(im(x))2((re(x))2+(im(x))2)(re(x2x+1)−1)−re(x))
sqrt((-im(x) + (im(x)^2 + re(x)^2)*im(sqrt(1 + 2*x)/x))^2 + ((1 + re(sqrt(1 + 2*x)/x))*(im(x)^2 + re(x)^2) + re(x))^2)*sqrt(((1 - re(sqrt(1 + 2*x)/x))*(im(x)^2 + re(x)^2) + re(x))^2 + ((im(x)^2 + re(x)^2)*im(sqrt(1 + 2*x)/x) + im(x))^2)*exp(i*atan2(((im(x)^2 + re(x)^2)*im(sqrt(1 + 2*x)/x) + im(x))/(im(x)^2 + re(x)^2), (-re(x) + (-1 + re(sqrt(1 + 2*x)/x))*(im(x)^2 + re(x)^2))/(im(x)^2 + re(x)^2)) + i*atan2((-(im(x)^2 + re(x)^2)*im(sqrt(1 + 2*x)/x) + im(x))/(im(x)^2 + re(x)^2), (-re(x) - (1 + re(sqrt(1 + 2*x)/x))*(im(x)^2 + re(x)^2))/(im(x)^2 + re(x)^2)))/(im(x)^2 + re(x)^2)^2