Find the Laplace transform of eat cos(3t) and eat sin(Bt) using the complex expo- nential and Euler's formula. i. Using the definition of the Laplace transform, find {eat} where a = a + Bi. ii. Use Euler's formula to compute the Laplace transform of eat (cos(3t)+i sin(3t)). Write your solution as the sum of real and complex parts. iii. Find the Laplace transform of eat cos(Bt) and eat sin(8t) by using the work from (ii) and the properties of the Laplace transform.