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what is i in the answer?

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Si So
Si So on 6 Jan 2021
Commented: Paul on 30 May 2024
I don't know what is i in the answer of my script. Complex number? how can I simplify it? I need to get rid of i.
syms x(t) s
Dx = diff(x(t),t);
ans =
- (s*laplace(x(t), t, s - 1i)*1i)/2 + (s*laplace(x(t), t, s + 1i)*1i)/2 - laplace(x(t), t, s - 1i)/2 - laplace(x(t), t, s + 1i)/2
Thank you for helping me
VBBV on 30 May 2024
@Si So you could simplify the equation and then use lapplace term by term
syms x(t) s
Dx = diff(x(t),t);
L = laplace(laplace(sin(t),t,s)*Dx,t,s)
L = 
Paul on 30 May 2024
What is the mathematical justifcation for this solution?
syms x(t) s
Dx = diff(x(t),t);
Consider the inner term
ans = 
What does it mean to mutiply of function of t with a function of s (in the context of this problem)?
Is there a reference for a property of the Laplace transform that says ( * means multiplication)?
L(f(t)*g(t)) = L(f(t))*g(t)
%L = laplace(laplace(sin(t),t,s)*Dx,t,s)

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