Question: Using Euler's formula, e^i theta = cos theta + i sin theta, show the following are true: e^i theta - e^-i theta/2i = sin theta,

Using Euler's formula, e^i theta = cos theta + i sin theta, show the following are true: e^i theta - e^-i theta/2i = sin theta, e^i theta + e^-i theta/2 = cos theta.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

A rotation matrix R is a 3 times 3 matrix which describes the relative orientation of two objects, for example the orientation of the nose and wings of an aircraft relative to the surface of the...

1. find the exact value of each of the following. In each case, show your work and explain the steps you take to find the value part 1: sin 17pi/6 a. use the fact that there are 2 pi radians in each...

MATLAB ASSIGN 1- Follow Directions and Complete. Will Thumbs Up! Directions: Unless otherwise specified, your write-up should contain the MATLAB input commands, the corresponding output, and the...

Complete following questions using Matlab. Equations 2.6 and 2.7 are given in last picture. 1. Write two functions to provide the rotation matrix around the x and y axes Using the provided templates...

Complete following questions using matlab 1. Write two functions to provide the rotation matrix around the x and y axes Using the provided templates write 2 functions that will return the basic...

the angle of elevation theta of the sun and sky at any latitude L is calcuclated with the formula sin theta cos d cos I cos w sin D sin L W is the number of raidans the earth has roated through since...

Hello! Just 3 quick problems. For number 29, please answer the question with a full explanation. I have attached below the blank question 29, which is the question you have to answer, and an example...

Many of MATLAB's ODE solvers for stiff systems (such as ode 15s) use numerical differentiation formula (NDF) methods, which are implicit schemes that generalize backward differentiation formula (BDF)...

Hello! For problems number 22 and 25 below, I just need you to check my answer and tell me which one is correct, I do not need an explanation. Let's look at the function f(x) = * -2 x 3 - 4 We will...

Jenna Suarez, the controller for Arben Company, has faced the following situations in the past two weeks: a. Ben Heald, head of production, wondered whether it would be more cost effective to buy...

Write down in terms of the absolute errors ?I and ?b in I and b respectively expressions for the absolute errors in the following quantities: The moment of inertia of a bar, length I and breadth b....

Question 5 In terms of their distribution strategies, countries differ along three main dimensions. These are end - user identification, channel integration, and transportation strategy. retail...

For f (x) = cos'r + sin"x; which of the following doesn't holds good? (A) Fundamental period of f(x) is (B) y = f(x) is symmetric about origin (C) f(x) is even function (D) The graph of y = f(x) is...

Given a triangle ABC with sides a = 7, b = 8 and c = 5. If the value of the expression sin A) ( cot) can be expressed in the form where p, q E N and is in its lowest form find unit place of p+q...

The number of integers in the domain of f (7) = log (5 (2) [e]) is (1) represents greatest integer function) Backspace 7 8 9 4 56 1 2 3

The radius of the circle touching incircle of an equilateral triangle of circumradius 6 unit, externally and its two sides, is r, value of (r), [ ] represent GIF Backspace 7 8 9 4 5 6 1 23

0.2 M; 100 ml NAOH is mixed with 0.4M; 100 ml HCI solution. Determine energy released during the reaction. H (aq) + OH (aq) H,0 (1) AH = -57.5 KJ mol-1 (A) 1150 J (B) 1150 KJ (C) 2300 J (D) 2300 KJ

Determine if the overhead allocated to the product relates to a single plantwide overhead rate method, multiple production department factory overhead rate method, or activity-based costing...

Imagine you work for a large global company in human resources. You are faced with some special staffing needs for a few of the departments that you serve. You know that the people youre looking for...

When you go looking for a job after graduation, what sources do you expect to use? Why? AppendixLO1

The emphasis on leased or temporary employees in an organization will only lead to a decrease in employee morale. These employees come in, do their jobs, then leave it up to the full-timers to handle...