Question

How to calculate laplace transform of complex roots?

Answer 1

Answer:

please mark as brainliest

Step-by-step explanation:

I have been asked to apply inverse laplace to this:

(4s+5)s2+5s+18.5

What I have done is; I found the roots of denominator which are :

(−5−7i)/2

and

(−5+7i)/2

Then I factorized the denominator as :

(4s+5)(s+(5+7i)2)(s+(5−7i)2)

Then i split this fraction to sum of two different fractions through;

(A)(s+(5+7i)2)

(B)(s+(5−7i)2)

Then I found A and B as ;

A=2+35i49

B=2−35i49

At the and , Inverse Laplace took this form ;

(2+35i49)(invLaplace(1s+5+7i2))+(2−35i49)(invLaplace(1s+5−7i2))

When I took the inverse laplace of these, the result was;

(2+35i49)((e)(−3.5i−2.5)t)+(2−35i49)((e)(3.5i−2.5)t)

I verified this result from Wolfram Alpha and Mathematica. But my guest professor insists this is not the solution and he gave me 0 points. He insists the solution includes cosines and sines. I explained him if he uses Euler Identity on these exponents the result will become his result but he refuses and says only way to solve this is to use Laplace tables.

I do agree making the denominator a full square and use Laplace table is the easier and cleaner solution. But isn't this also a solution? Thanks.