Problem with the product of complex numbers

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I calculated the equivalent impedance of an RLC circuit, and I would like this one to be completely resistive (complex part equals to 0). So I declared my variables as 'syms' and I used the function 'solve' to obtain the equivalent impedance litterally like:
% syms R X Y Z
% Zeq=solve('(R+i*X)*(-i*Y)/(R+i*X-i*Y)=Z',Z)
The problem is that Matlab gives me a solution like this:
%Zeq =
% -(Y*(R + X*i)*i)/(R + X*i - Y*i)
But I would like something like: Zeq = A + i*B.
Could anyone help?

Accepted Answer

Jonathan Epperl
Jonathan Epperl on 24 May 2013
Probably simplify(Zeq) will do that.
clement on 24 May 2013
Thanks it's working! But now I've got another problem... When I multiply tne numerator of my fraction by the complex conjugate of the denominator, Matlab gives me this:
%sol = -Y*(R + X*i)*(X - Y + R*i)
instead of A + i*B. And this time 'simplify', or 'factor' don't work.
Walter Roberson
Walter Roberson on 24 May 2013
expandsol = expand(sol);
A = real(expandsol);
B = imag(expandsol);

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More Answers (1)

Walter Roberson
Walter Roberson on 24 May 2013
You cannot do that unless you add the assumption that the variables are real-valued
syms R X Y Z real
Zeq = simplify(solve((R+i*X)*(-i*Y)/(R+i*X-i*Y)-(Z),Z));
A = simplify(real(Zeq));
B = simplify(imag(Zeq));
A + B*i
Walter Roberson
Walter Roberson on 25 May 2013
Before R2011b, "==" was processed as a logical relationship to be evaluated and the result of the logical evaluation to be passed into solve(). But those versions also did not know how to compare a symbol (with any content) against a number, so the expression would generate an error... unless, of course, A was a number instead of a symbol.
Jonathan Epperl
Jonathan Epperl on 25 May 2013
I see, I didn't know that -- so A-50 is the more robust syntax...

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