What am I doing wrong here? I am trying to recreate following highlighted equations in the table.

ep = linspace(0,1);
m1 = 1.5; m2 = 3.8;
ep0= 1; alpha = 0.785; epp = 0.11;
qep = (2.76*ep*cosh((3*ep)-1.92));
I1 = ep.^ m1;
I2 = ep.^ m2;
I3 = ep*((ep-epp)/(ep0-epp)).^alpha;
I6 = 1-(qep*((3*(1-ep))/(3-ep)));
Hold on
plot(ep,I1)
plot(ep,I2)
plot(ep,I3)
plot(ep,I6)
Hold off

Answer 1

[Paul Hoffrichter]

clc; clear; clf
ep = linspace(0,1);
m1 = 1.5; m2 = 3.8;
ep0= 1; alpha = 0.785; epp = 0.11;
qep = (2.76*ep.*cosh((3*ep)-1.92));
I1 = ep.^ m1;
I2 = ep.^ m2;

zz = (ep-epp)/(ep0-epp);
zza = zz .^ alpha; % zza is complex
I3 = ep .* zza;

I6 = 1-(qep*((3*(1-ep))/(3-ep)));

hold on
plot(ep,I1);
plot(ep,I2)
plot(ep,I3) % This is Line 18 - usually do not plot a complex vector like this

plot(ep,I6)
hold off

warning:

Warning: Imaginary parts of complex X and/or Y arguments ignored. 
> In Untitled (line 18) 

[Nissal Arachchige]

Thank you for the help

[Paul Hoffrichter]

Sure thing. Just curious.. Were you expecting complex numbers at Line 18?

[Nissal Arachchige]

No not at all. I was actually able to recognize my coading problem before you posted the answer and I got the same solution as you and the warning as well. I do not know why it does that. And I was supposed to recreate the follwing graph but ignore the points and the legend. I'm waiting for the feedback from my professor. I'll let you know if something intresting come up. Thanks again.

[Paul Hoffrichter]

I was a surprised at first about the complex numbers. But then I thought about what if alpha was 0.5 instead of 0.785. Then if x is a negative number, we have a purely imaginary result for x^(.5)=sqrt(x)= sqrt{(-1) * abs(x)} = 0 + j*sqrt(abs(x)). For other values of alpha between (0.5, 1.0), we get complex numbers.