Laplace Transform Homework Solutions Check

noreturn2
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Homework Statement


gr9fpdM.png


Homework Equations

The Attempt at a Solution


1. I got Y(s) = (15s +18)/(5s^2+s-2)

2. I got Y(s) = (7s - 7iw + 1)/((s+4)(5 - iw))

Was just wanting to make sure I solved these right. I would type it out but without formating, it will look messy.
 

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noreturn2 said:

Homework Statement


View attachment 224321

Homework Equations

The Attempt at a Solution


1. I got Y(s) = (15s +18)/(5s^2+s-2)

2. I got Y(s) = (7s - 7iw + 1)/((s+4)(5 - iw))

Was just wanting to make sure I solved these right. I would type it out but without formating, it will look messy.
I got the same as what you have for #1. Can you show your work for #2?
 
a6fea26b-c651-45c7-a73f-078346d087d5
34DGTLn.png
 

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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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