Using Euler's formula, state all possible values of the expressions:
A. e^(i3pi)
B. (1)^(1/4)
C. e^(1+i2)
D. arg(2-2i)
E. Arg(2-2i)
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Using Euler's formula, state all possible values of the expressions: A. e^(i3pi) B. (1)^(1/4) C. e^(1+i2)...
Time series analysis
1. (a) Use Euler's identity e¡θ-cos θ + i sin θ to prove that sin θ=-(eiO , 2i (b) Use the identities above and the formula for the sum of a geometric series to prove that if n is an integer and j E 1,2,... ,n} then TL TL sin-(2Ttj/n)- n/2 so long as J关[m/2, where Laj is the greatest integer that is smaller than or equal to x (c) Show that when j 0 we have...
Exercise7 Simplify the following expressions as much as possible. 100 200 777n log(i +i2)- i2 log(i + i-), CF i 101 50 l-25 50 d:- In(t +1) In
Exercise7 Simplify the following expressions as much as possible. 100 200 777n log(i +i2)- i2 log(i + i-), CF i 101 50 l-25 50 d:- In(t +1) In
3. Euler's Method (a) Use Euler's Method with step size At = 1 to approximate values of y(2),3(3), 3(1) for the function y(t) that is a solution to the initial value problem y = 12 - y(1) = 3 (b) Use Euler's Method with step size At = 1/2 to approximate y(6) for the function y(t) that is a solution to the initial value problem y = 4y (3) (c) Use Euler's Method with step size At = 1 to...
Problem 2. In this problem, we will use Euler's formula to derive some trigonometric identities. (a) Using Euler's formula and the property that ez+w = e ew for any complex numbers z and | W, show that cost + sin? t = 1. (Hint: Start with 1 = eit-it.) (b) Similarly, show that cos(2t) = cos? t – sint. (Hint: Start with cos(2t) = Re(ezit).) (c) Similarly, show that sin(2t) = 2 sint cost. (d) Similary, show that cos(3t) =...
(a) Sketch a 2D vertex-edge graph of the square pyramid shown below. Euler's formula: v+f=e+2 (b) The square pyramid has 5 faces and 5 vertices. How many edges does it have? (c) Label each geometric solid as possible or impossible. 8 vertices, 14 edges, 6 faces 7 vertices, 12 edges, 7 faces
Part B 1. (2 pts each) a. For n = 4, what are the possible values of n b. For 1 = 2, what are the possible values of ? c. If m is 2, what are the possible values for i? 2. (2 pts each) Write the condensed electron configurations for the following atoms, using the appropriate noble-gas core abbreviations: a. Cs, b. Ni, c. Se d. Cd,
C++ Euler's method is a numerical method for generating a table of values (xi , yi) that approximate the solution of the differential equation y' = f(x,y) with boundary condition y(xo) = yo. The first entry in the table is the starting point (xo , yo.). Given the entry (xi , yi ), then entry (xi+1 , yi+1) is obtained using the formula xi+1 = xi + x and yi+1 = yi + xf(xi , yi ). Where h is...
[3] A spin-1/2 particle is in the state IW) 1/311) +i2/3|). (a) A measurement is made of the x component of the spin. What is the probability that the spin will be in the +z direction? (b) Suppose a measurement is made of the spin in the z direction and it is found that the particle has m,#1/2. what is the state after the measurement? (c) Now a second measurement is made immediately after to determine the spin in the...
Using the data table below, calculate the values for the following expressions. Note that n represents the number of summations (i.e. when calculating Xx;, then n=3). X and are the means of the values being summed (i.e. when calculating 2x;, then X = [*;, then X = X,+X.). Record all answers in the Part IV worksheet of the Assignment 1 spreadsheet. (Each calculation is worth 2 marks). 1 2 4 5 6 7 3 22 х 14 19 35 16...
Normalize the following untyped applied lambda calculus expressions as much as possible using the call-by-value rules, showing all steps CLEARLY, please. TYPED answer is preferred. a) (λx. x * x) 1 b) (λx. x + 4) ((λy. y + 5) 3) c) (λf g x. g (f x)) (λa. a * a) (λb. b + 1 + 2) 3 d) (λf x. f (f (f x))) (λb. if b then false else true) true