MATLAB-finding roots and summations

[Dsab123]

Homework Statement

(all this is included in the attachment, btw)

p(z)=z^4+4.25*z^2+1

1. use MATLAB to find the four roots Ck of
p(z)= 0

2. For all complex constants ck (different than Ck) define the complex valued function
Z(t)= 4$$\Sigma$$k=1 ck*exp(Ck*t)

^^that is a sigma sign with variable k going from one to four

Homework Equations

p(z)=z^4+4.25*z^2+1
a=4.25

The Attempt at a Solution

Number 1 I can do fine, my code is as follows:

>> syms x
>> y=(x^4+4.25*x^2+1)
>> >> solve (y)
ans =
(-2)*i
2*i
-i/2
i/2

The problem is when I get to problem 2, because I have just about no idea of how to compute a sum in matlab. I've tried a for loop with k going from one to for, after naming each of the roots C1, C2, C3, C4.

Also, I'm having some trouble figuring out what it means by 'complex constants ck'..
sorry I'm not much help in understanding this haha.


3 and 4 i think I can figure out
Any help would be very much appreciated

 

[Mindscrape]

I don't do much with symbolic in Matlab, but something like this should work.

>> syms x
>> y=(x^4+4.25*x^2+1)
>> roots = solve (y)
Z=0;
syms t
for j=1:length(roots)
Z = Z + roots(j)*exp(roots(j)*t)
end