how to solve multi variable simultaneous equations

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Hi all,

Please help me wiht this, I am new to matlab.

I want to solve two equattions which has five variable, so I want to provide ranges for three variables and get all the solutions.

3 variable with ranges are x4, x5 and z4, and I want to find corresponding solution for z5 and G. (Actually I have a formula which I nedd to equate with the real and imaginary part of a complex number)

I have tried this way-

x4=pi/36:pi/9:pi/2;
x5=pi/6:pi/9:pi/2;
z4=60:20:80;
for a=1:length(z4)
    for b=1:length(x4)
        for c=1:length(x5)
            
            ZL=61.5-1i*47.4; 
            YL=1/ZL;           %  to be equated with its conjugate
            GL=real(YL);
            BL=imag(YL);
            
            syms z5 real
            syms z55 real
            assume( z5 > 0)
            syms G real
            assume( G>0)
            y4=1./z4;y5=1./z5;
            
            ya(a,b)= -1i.*y4(a).*cot(x4(b))     % Formula -I
            yb(c)=vpa((y5).*(G + 1i.*y5.*tan(x5(c)))./(y5+ 1i.*G.*tan(x5(c))))     %Formula-2
            
            yeq(a,b,c)=ya(b)+yb(c)     %sum
            yeqR=real(yeq)
            yeqI=imag(yeq)
            
            eqn=[yeqR==GL, yeqI==-BL]
            var=[G z5]
            
            
            s=solve(eqn, var)
            
            G1=s.G
            z55=s.z5
            
        end
        
    end
end

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Hedayat 2018-11-13

Thanks KSSV,

below is the eqns, I have 5 variables and two eqns, so I have to assume 3 variables. (Later I will see if solutions are feasable or not)

ya= - i*y4*cot(x4)

yb= (y5 * (G+ i *y5* tan(x5))) / (y5+ i G* tan(x5) )

yeq=ya+yb

yL=1/(61.5-i*47.4)

Solve(yeq=yL*)

KSSV 2018-11-13

What are the unknowns in the above? YOu can solve it with hand first..equate complex and real parts...and these two parts should be solved for unknowns.

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Hedayat 2018-11-13

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Thank you again KSSV,

I need values for G and y5, and I want to sweep y4,x4 and x5, as I mentioned in main post. it wil not always yield a desired solutions. For example, I need a value of y5 in the range of 20-120 and G>0. Plus,based on these results, I have to add other complicated equations that too have some constraints , and this is why I am avoiding hand calculations.

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