Cs6515 Exam 1 Prep Verified Solutions

1.) what is the product of the roots of unity? 2.) What about the sum? 3.) What is the sum of Aeven? 4.) what is the sum of Aodd? {Ans: 1.) if it is even, then it is == 1 if it is odd, then it is == -1 2.) The sum is == 0. This is because (ω_n)^0 == 1 and (ω_n)^(n/2) == -1. These cancel each other out. So if you go through the whole sequence.. it eventually becomes 0. 3.) (n/2) * 1 4.) (n/2) * -1}what is the significance of z = a + bi {Ans: it can describe a point in a cartesian plane}if you are presented with a coins (1,5,6,8) and your knapsack is k = 11, what is the minimum number of coins, what would be the computational time, and what is the recurrence? {Ans: https://www.youtube.com/watch?v=Y0ZqKpToTic}Consider the n-th roots of unity for n =16. WHat is ω_16 in polar coordinates? {Ans: At point 0, polar coordinates are (r, theta) == (1, 2pie/2), if n = 16, then it becomes - (1, 2pie/2)^16 == (1,2pie/16) == (1, pie/8)}How do you convert the cartesian coordinates (a,b) to polar coordinates? {Ans: