How to find the complex root for this equations

Hi guys!

I'M new using Matlab .

i'm trying to finding the roots for an effective permittivity equation in two form Quadratic and Nonlinear and it Should have the Same solution

any suggestion how to solve equations and find roots.

%Quadratic Equation

function ere= roots

p=[0.23,0.25,0.27]; % concentration of sample

er1=(1+1.8*10^14*i); % Phase one Permittivity

er2=(2.5+2.5*10^-3*i); % Phase two Permittivity

ere=(1./4).*(((3.*p-1).*er1)+((2-3.*p).*er2)+((((3.*p-1).*er1)+((2-3.*p).*er2)).^2+8.*er1.*er2).^0.5);

% effective permittivity

plot(p,ere)

end

Nonlinear Equation

function fval=eqns(ere)

P=[0.23,0.25,0.27];

er1=(1+1.8*10^14*1i);

er2=(2.5+2.5*10^-3*1i);

fval=((P).*((ere-er1)./(er1-2.*ere)))+((1-P).*((ere-er2)./(er2-2.*ere)));

plot(p,ere)

end

Answer 1

[Alex Mcaulley]

First, one important suggestion: Don't call your function as one Matlab function (roots, in fact is the one that you need to call).

After that, the equation (3) is trivial, you get the value of ere directly as you have in your function:

p = [0.23,0.25,0.27]'; % concentration of sample 
er1 = (1+1.8*10^14*i); % Phase one Permittivity
er2 = (2.5+2.5*10^-3*i); % Phase two Permittivity 
ereEQ3 = (1./4)*(((3*p-1)*er1) + ((2-3*p)*er2) + ((((3.*p-1)*er1) + ((2-3*p)*er2)).^2+8*er1*er2).^0.5);

For the other equation (2), yo need to obtain the roots of the second orden polynomial. One option is to use the roots function. (Note that you will obtain 2 solutions for each value of p, and only one is the same than the one obtained with the previous equation).

pol = [2+p*0, (-2+3*p)*er2 + (1-3*p)*er1, -er1*er2+p*0];
ereEQ2 = arrayfun(@(i) roots(pol(i,:)),1:numel(p),'uni',0);

[Ammar Ahmed]

hanks for replying i tried to use your command

pol = [2+p*0, (-2+3*p)*er2 + (1-3*p)*er1, -er1*er2+p*0];

ereEQ2 = arrayfun(@(i) roots(pol(i,:)),1:numel(p),'uni',0);

but it give me Error

Error using roots

Too many input arguments.

Error in @(i)roots(pol(i,:))

[Alex Mcaulley]

It seems that you still have your function called roots. Change the name of your function, run this command in the command window:

clear all

And try to execute my code

Answer 2

[Ammar Ahmed]

thanks for replying i tried to use your command

pol = [2+p*0, (-2+3*p)*er2 + (1-3*p)*er1, -er1*er2+p*0];

ereEQ2 = arrayfun(@(i) roots(pol(i,:)),1:numel(p),'uni',0);

but it give me Error

Error using roots

Too many input arguments.

Error in @(i)roots(pol(i,:))