Use the power series representation of eu centered at 0, to show why Euler's formula ei = cos + i sin is true. (You should have done this in class, but it's such an amazing result that we want you to work through it yourself.) 3. When solving differential equations of the form x + bx + cx = 0, we sometimes end up looking at functions like 5+3i 2 e2it + 53i 2 e2it. Unfortunately, a function expressed in this form is not terribly useful; for instance, it's hard for us to graph it. In this problem, you'll see how to rewrite this function in a more friendly form. (a) Use Euler's formula to express e2it in terms of cos(2t) and sin(2t). (b) Use Euler's formula to express e2it in terms of cos(2t) and sin(2t). (c) Which of the following statements are true? (There are 2.) i. cos(2t) = cos(2t) ii. sin(2t) = sin(2t) iii. cos(2t) = cos(2t) iv. sin(2t) = sin(2t). (d) Use your answers to (b) and (c) to express e2it in terms of cos(2t) and sin(2t). (e) Express 5+3i 2 e2it + 53i 2 e2it in terms of cos(2t) and sin(2t). (Please