Help with finding zeros of a complex function

Hi there.

I have been given a task, where i need to find the zeros of the following complex function:

I have tried using fzero, but can't really make it work. I already know the answer to the task, which is that there are zeros in:

and in

Do you guys know a way to make Matlab calculate this?

Thanks a lot!

Answer 1

[Star Strider]

If you want reasonably close results for the roots:

g = @(z) z.*exp(z)./((z-pi).*cos(z));

zv = linspace(-10, 10, 5000)*pi;
gz = g(zv);

zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                            % Returns Approximate Zero-Crossing Indices Of Argument Vector
idxv = zci(gz);

for k1 = 1:numel(idxv)
    b = [zv(idxv(k1)-1) 1; zv(idxv(k1)) 1] \ [gz(idxv(k1)-1); gz(idxv(k1))];    % Linear Fit Near Zero-Crossing
    rt(k1) = -b(2)/b(1);                                                        % Interpolate To Precise Value
end

figure
plot(zv, g(zv))
hold on
plot(rt, zeros(size(rt)), 'xr')
hold off
grid
ylim([-5, 5])

fprintf('\nAs multiples of ‘pi’:\n')
fprintf('\t%8.2f\n', rt/pi)

fprintf('\nAs multiples of ‘n’:\n')
fprintf('\t%8.2f\n', (rt-pi/2)/pi)

Using fzero, the loop becomes:

for k1 = 1:numel(idxv)
    rt(k1) = fzero(g, [zv(idxv(k1)-1),zv(idxv(k1)+1)]);                           % Use ‘fzero’ To Interpolate To Precise Value
end

with much more precise results.

It is likely not possible to do this without a loop, simply because it is necessary to iterate over all the zero-crossings.

[madhan ravi]

+1 an absolut genius!

[Star Strider]

Thanks! (Although ‘genius’ is probably something of an exaggeration!)

[madhan ravi]

:-)

Answer 2

[madhan ravi]

Use fsolve(), vpasolve() or solve() and ezplot() or fplot() to view where the zero occurs..

[madhan ravi]

Mikkel Jorgensen's answer moved here for consistency:

Hi. Thanks for the answer.

I just tried that - but am getting the wrong result. I have inserted a picture of what i have done:

[madhan ravi]

First thing that you need to know is uploading a picture is never useful.. upload your code

Second thing what do you observe from the graph?

Third thing why do you say the result is wrong?