Suggestions on solving this complex-vector-nonlinear system of equations in MATLAB

I have this equation in here:

W is a vector with a component in the real numbers and one in the imaginary numbers (At the end it's just like an x component and y component), same with Z and delta 2 and delta 3.

I want to know about ways to solve this using Matlab or something in Toolbox, I already tried to debunk the equation to get a 4x4 non linear equation and I solved it

clc
clear all
syms wx zx wy zy
alfa2=205*(pi/180);
alfa3=55*(pi/180);
beta2=39*(pi/180);
beta3=94*(pi/180);
delta2x=0.2;
delta2y=1.2;
delta3x=-0.75;
delta3y=2.5;
E1=wx*cos(beta2)-wx+wy*sin(beta2)+zx*cos(alfa2)-zx+zy*sin(alfa2)-delta2x;
E2=wx*sin(beta2)+wy*cos(beta2)-wy+zx*sin(alfa2)+zy*cos(alfa2)-zy-delta2y;
E3=wx*cos(beta3)-wx+wy*sin(beta3)+zx*cos(alfa3)-zx+zy*sin(alfa3)-delta3x;
E4=wx*sin(beta3)+wy*cos(beta3)-wy+zx*sin(alfa3)+zy*cos(alfa3)-zy-delta3y;
result=vpasolve([E1,E2,E3,E4], [wx,zx,wy,zy],[1,1,1,1])

result = struct with fields:
    wx: -271.19634086868016733135733625065
    zx: -47.962983642784204963593838989701
    wy: -272.97936518137371030777492742679
    zy: -47.612878234770207671139896881546

I wanna know any other way to solve it in Matlab

Answer 1

[Torsten]

This is a simple linear system of equations in the unknowns W and Z:

alpha2 = 205*(pi/180);
alpha3 = 55*(pi/180);
beta2 = 39*(pi/180);
beta3 = 94*(pi/180);
delta2x = 0.2;
delta2y = 1.2;
delta2 = delta2x + 1i*delta2y;
delta3x = -0.75;
delta3y = 2.5;
delta3 = delta3x + 1i*delta3y;
A = [exp(1i*beta2)-1.0,exp(1i*alpha2)-1.0 ; exp(1i*beta3)-1.0,exp(1i*alpha3)-1.0];
b = [delta2;delta3];
sol = A\b;
W = sol(1)

W = 1.5417 - 0.8889i

Z = sol(2)

Z = 0.0044 - 0.0176i

[José David Castillo Blanco]

Thanks for the aswer, didn't know it was linear.

[José David Castillo Blanco]

Don't worry mr, I already did it, I leave the code if anyone is interested

clc

clear all

syms W Z

alfa2=205*(pi/180);

alfa3=55*(pi/180);

beta2=39*(pi/180);

beta3=94*(pi/180);

delta2=0.2+1.2i;

delta3=-0.75+2.5i;

E1=W*(exp(1i*beta2)-1)+Z*(exp(1i*alfa2)-1)-delta2;

E2=W*(exp(1i*beta3)-1)+Z*(exp(1i*alfa3)-1)-delta3;

result=vpasolve([E1,E2],[W,Z])

Thanks for the help