Cauchy-Riemann Equations using Matlab

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Romuel Josue Miranda
Romuel Josue Miranda 2021 年 5 月 4 日
Good day! I would like to ask your help to correct my matlab codes. I think there is something wrong and I need someone to check my work. Thank you.
Matlab code:
For a:
syms z x y Z;
fz=(z^2)-(z)^2
expand(fz);
Z=x+j*y;
du=diff(Z^6/2 + (3*Z^4)/2,x);
dv=diff((3*Z^2)/2 + 1/2,x);
du=subs(du,x,z);
du=subs(du,y*1i,0);
f1=factor(dv)
dv=f1(1:1)*z;
dz=du+dv;
simplify(dz)
ans =
3*z*(z^2 + 1)^2
For b:
syms x y
u=x^2-y^2-8*x*y-3*x-2;
v=2*x*y+4*x^2-4*y^2-3*y;
ux=diff(u,x);
ux=subs(ux)
ux =
2*x - 8*y – 3
uy=diff(u,y);
uy=subs(uy)
uy =
- 8*x - 2*y
vx=diff(v,x);
vx=subs(vx)
vx = 8*x + 2*y
vy=diff(v,y);
vy=subs(vy)
vy =
2*x - 8*y - 3
dw = vy+vx*i
- 3 + x*(2 + 8i) - y*(8 - 2i)

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