Question: Show that 1/i = -i, e -ix = cos x - i sin x, e ix + e -ix = 2 cos x, e ix

Show that 1/i = -i, e-ix = cos x - i sin x, eix + e-ix = 2 cos x, eix - e-ix = 2i sin x, eikx = cos kx + i sin kx.

Step by Step Solution

★★★★★

3.32 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

First write out the general form of the solution in algebraic notation x iy 2m Next well find two va... View full answer

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 Advanced Engineering Mathematics Questions!

Q:

Show that 1 is orthogonal to cos kx and sin kx in [- , ] for k 1.

Q:

Show that the 2n + 1 complex exponentials eikx for k = - n, - n + 1........ - 1, 0, 1,... ,n, form an orthonormal basis for the space of complex-valued trigonometric polynomials under the Hermitian...

Q:

Show that cos jx is orthogonal to cos kx in [- n, n] for j k, j, k 1.

Q:

Python script please Please use exp(ix) function with complex value. and the script has to be the simplest Compute the value of eix using Python's exp function and display the value to 14 decimal...

Q:

I need help plotting this function on MATLAB using while loops. Please help me with the MATLAB code. (ix) (ix) (ix) eix = 1+ ix + + (ix)3 3! + + (ix)" 5! + (ix)6 6! (ix)" 7! + + +. 2! 4! 8! X2 27 X8...

Q:

1 Multivariable functions and vector geometry Due date and time: Wednesday, June 7th at 9:30 AM in lecture Please ensure that you have read and understood the document \"Homework Guidelines" on the...

Q:

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

Q:

1. Find the area of the sector of a circle with diameter 30 feet and an angle of . radians. Round your answer to four decimal places. A = Number ft 2 Show your work and explain, in your own words,...

Q:

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

Q:

Math 1242-006 Dr. Taylor Test I Review Name: ____________________ HW#1 Chapter 5.1 and 6.1 (Print Last Name First!) You must show all your work in the provided space to receive credit - even on the...

Q:

Mr. Roads is a 70-year-old man who was admitted to an inpatient psychiatric unit after displaying behavioral aggression. Before his admission, he was screaming at anyone who came near him. During his...

Q:

List disadvantages of using a single directory.

Q:

The circumference of a circular disc is 39 cm. Work out the diameter of the disc. Give your answer correct to the nearest millimetre. For questions, use the button on your calculator.

Q:

=+What is one thing you cant live without while working in social media?

Q:

The cumulative frequency for the top row in a frequency distribution is equal to ____.

Q:

If one has ____ -level data in a frequency distribution, it should be organized in some logical fashion.

Q:

The ____ column in a frequency distribution is a restatement of the information in the cumulative frequency column.

Q:

Suppose the nominal returns on Beaver Company's stock over the past five years are: 20%, -12%, 17%, 20%, and 10%. The average inflation rate over this period was 1.7% and the average T-bill rate over...

Q:

Sharon is considering the purchase of a car. after making the down payment, she will finance $ 22,909. sharon is offered three maturities. on a four-year loan, sharon will pay $569.87 per month. on a...

Q:

V. My bank requires a 10% down payment on my home loan. Assuming the down payment amounts to $40,000, how much must I save monthly beginning today to accumulate the above amount in 5 years at 6%...