what is i in the answer?

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Si So 2021-1-6

评论： Paul 2024-5-30

Hello,

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);
laplace(sin(t)*Dx,t,s)

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 2024-5-30

@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 2024-5-30

What is the mathematical justifcation for this solution?

syms x(t) s
Dx = diff(x(t),t);

Consider the inner term

(laplace(sin(t),t,s)*Dx)

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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