Hello, can MATLAB solve equations like the one below? I mean, can MATLAB find the conditions for z that satisfy this relationship, instead of just numerical solutions?

Answer 1

[Fangjun Jiang]

https://www.mathworks.com/products/symbolic.html

Answer 2

[Walter Roberson]

If the * stands for conjugation, then it seems to be universally true for finite values

syms z
eqn = sqrt(conj(z)) - conj(sqrt(z));
sol = solve(eqn, 'returnconditions', true)

Warning: Unable to find explicit solution. For options, see help.

sol = struct with fields:
             z: [0x1 sym]
    parameters: [1x0 sym]
    conditions: [0x1 sym]

F = @(z12) sqrt(z12(:,1) - z12(:,2)*1i) - conj(sqrt(z12(:,1) + z12(:,2)*1i));
points = [randn(10,1), randn(10,1)];
Fp = F(points);
mask = abs(Fp) < 1e-10;
[points(mask,1), points(mask,2)]

ans = 10×2

-0.6113 0.7367 -1.7766 0.4581 -0.0074 -1.1701 -0.7251 -0.7878 -0.2333 -0.7190 -0.2703 0.9049 -0.2190 -0.0145 2.1642 0.6960 -0.2029 -0.0401 1.6399 0.6714

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Fp

Fp = 10×1

0 0 0 0 0 0 0 0 0 0

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subs(eqn, z, points(:,1)+points(:,2)*1i)

ans =