Problem with the product of complex numbers

Hello,

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?

Thanks

Answer 1

[Jonathan Epperl]

Probably simplify(Zeq) will do that.

[clement]

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]

expandsol = expand(sol);
A = real(expandsol);
B = imag(expandsol);

Answer 2

[Walter Roberson]

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

[clement]

Thanks. I have another question.

Now I would like 2 conditions: A=50 et B=0 in order to have a 2 equations on X. The expression of A being:

 %A = (R*Y^2)/(R^2 + X^2 - 2*X*Y + Y^2)

When I use the function 'solve' written like this:

 % S1=solve('(R*Y^2)/(R^2 + X^2 - 2*X*Y + Y^2)=50',X)

the code works, but when I write it like this:

% S1=solve('(A=50',X)

it doesn't...

Do you know why?

Because the aim is to calculate everything automatically, so if I have to copy/paste my result the program is useless...

Thanks

[Jonathan Epperl]

   S1 = solve(A==50,X)

You need two equal signs ==, one equal sign = assigns a value to the variable on the left, which is not what you want to do here.

[clement]

With this syntax, it tells me that X equals to 5, which is not possible because I didn't give any values to X and Y...

Anayway, I did the calculations on paper and the result should be:

% X = Y*(50-R)/50

[Jonathan Epperl]

That is curious. I can confirm neither of this:

 syms R X Y real
A = (R*Y^2)/(R^2 + X^2 - 2*X*Y + Y^2)
solve(A==50,X)
simplify(ans)

yields

ans =

 Y + (-2*R*(- Y^2 + 50*R))^(1/2)/10
 Y - (-2*R*(- Y^2 + 50*R))^(1/2)/10

You might have assigned X or Y somewhere earlier in your session, if you want to make sure that they are "pristine" when you declare them as symbolic variables, do this

clear X Y R
syms X Y R real

[clement]

It works when I do:

    S10=solve(A-50,X)

[Jonathan Epperl]

S10=solve(A-50,X)

and

S10=solve(A==50,X)

should do the exact same thing, I can't think of one reason why one should work when the other doesn't.

What version of the Symbolic Toolbox are you using (command ver symbolic) ?

[Walter Roberson]

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]

I see, I didn't know that -- so A-50 is the more robust syntax...