plotting real and imaginary parts

I was working the following questions and got into some difficulties. I don't think what I have written so far is correct and I don't know how to continue. I have worked until question C. There is a misprint in the empirical characteristic function. The i should be a j. It should be taken that sigma is 4 throughout these questions.

%Question A
clear all
clc

a=random('normal',4,1,100,1);
b=random('normal',4,1,300,1);
c=random('normal',4,1,1000,1);

%Question B & C

% initializing vectors to store points
first = zeros(1,100);
second = zeros(1,300);
third = zeros(1,1000);
f = zeros(1,7);

% setting count as 1 to initialise the figures
count = 1;

% we will vary t from -3 till 3 and obatin a plot for each
for t = -3:1:3
    
    % loop to get points of phi_n_(t) using vector a of size 100
    for j = 1:100
    first(1,j) = (1/size(a,1))*(cos(t*a(j,1)) + sqrt(-1)*sin(t*a(j,1)));
    %real and imaginary parts of the points obtained above
    realfirst = real(first);
    imfirst = imag(first);
    end
    
    % loop to get points of phi_n_(t) using vector b of size 300
     for k = 1:300
    second(1,k) = (1/size(b,1))*(cos(t*b(k,1)) + sqrt(-1)*sin(t*b(k,1)));
    %real and imaginary parts of the points obtained above
    realsec = real(second);
    imsec = imag(second);
     end
     
     % loop to get points of phi_n_(t) using vector c of size 1000
     for h = 1:1000
    third(1,h) = (1/size(c,1))*(cos(t*c(h,1)) + sqrt(-1)*sin(t*c(h,1)));
    %real and imaginary parts of the points obtained above
    realthird = real(third);
    imthird = imag(third);
     end
     
    % plot of phi_(t) 
    f(1,count) = exp((sqrt(-1)*1*t) - (t/2));
    realf = real(f);
    imf = imag(f);
    
    figure(count)
    % plot(sum(realfirst),sum(imfirst),'r*',sum(realsec),sum(imsec),'b*', sum(realthird), sum(imthird),'g*',realf,imf,'y')
    plot(realfirst,imfirst,'r*',realsec,imsec,'b*',realthird,imthird,'g*',realf,imf,'y')
    % points in red are for vector a of size 100
    % points in blue are for vector b of size 300
    % points in green are for vector c of size 1000
    % can be seen that the yellow line of phi_(t) converges towards the
    % centre of the circles plotted of phi_n_(t)
    count = count+1;
end

[darova]

So you have

and function

so what is the problem?

t = -3:0.1:3;
phi = exp(1i*mu*t-sigma^2*t/2);
plot(t,imag(phi),t,real(phi))

simple?

Answer 1

[kalaiselvi p]

t = -3:0.1:3;

phi = exp(1i*mu*t-sigma^2*t/2);

plot(t,imag(phi),t,real(phi))