There is no fzero() command that can work. You have a vector of 3 equations that are inconsistent with each other. And if you were to break it up into three different equations, then you would encounter the problem that fzero() can only deal with real-valued functions of a single real-valued variable.
fsolve() can deal with complex valued functions.
A standard trick to convert complex inputs into real inputs is to separate into real and imaginary components, such as
f2 = @(x) x.^2 + 1;
f = @(x) f2(x(1) + 1i*x(2));