Question: Show that (sin (x+i y)=sin x cosh y+i cos x sinh y) using trigonometric identities and the exponential forms of these functions.

Show that \(\sin (x+i y)=\sin x \cosh y+i \cos x \sinh y\) using trigonometric identities and the exponential forms of these functions.

Step by Step Solution

★★★★★

3.38 Rating (145 Votes )

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 Mathematical Methods For Physicists Questions!

Q:

I need these charts filled in using the information given Instructions Analysis Ledger Trial Balance Greenwald and Mass developed a business and plan to begin by offering clinics for basic outdoor...

Q:

The following balance sheet for the Los Gatos Corporation was prepared by a recently hired accountant. In reviewing the statement you notice several errors. Cash Accounts receivable Inventory...

Q:

If a U.S. resident just sold his portfolio in the British market and realised a 15% return (in GBP) during a period when the USD depreciated 5% against GBP, what is the investor's realised return in...

Q:

In Sec. 34, use expressions (13) and (14) to derive expressions (15) and (16) for |sin z|2 and |cos z|2. (13) sin z = sin x cosh y + i cos x sinh y, (14) cos z = cos x cosh y i sin x sinh y, where z...

Q:

I.8.2 Show that cos 22 = cos + sinhy, where =+iy. Find all zeros and periods of cos z. Solution. Use trigonometric formulas from page 29 and 30 in CA we have, cos = cos(x + y) = cos r cos (iy)-sin r...

Q:

DO EVERY QUESTION PLEASE AND SHOW YOUR WORK! TIDY HANDWRITING AND CIRCLE THE ANSWERS BY TONIGHT THANK YOU SO MUCH 5. Given: g(x) = ex tan x a) Which rule should be used to find the derivative?...

Q:

7/4/23, 11:16 PM Homework 8.7-Anh Nguyen Use a table of integrals to determine tv7t+ 19 at. Click here to view page 1 of the integral table. " Click here to view page 2 of the integral table. 14...

Q:

100. Videography A television camera at ground level films the lift-off of a space shuttle at a point 750 meters from the launch pad (see figure). Let @ be the angle of elevation to the shutthe and...

Q:

Using trigonometric identities, show that the basis functions in the series in Eq. (11.1) are periodic with period 2L. () +> bn sin x (). f (x) a0 +a cos . n=1 n=1 (11.1)

Q:

= n a X 2 n 2 2 EnE 2 ma3. ( /24 pts) Suppose an infinite square well potential is given by c D (a) (4 pts) Sketch the potential. (b) (12 pts) As we saw in class, the general solution to the infinite...

Q:

5. /16 pts) A particle in a one-dimensional, infinite square well of length L has the initial, normalized wave function CO I (x, 0) = (a) (8 pts) Find I(x, t). (b) (4 pts) What is the probability of...

Q:

In the Appendix to Chapter 4, the equations of the IS and LM curves are given as follows: IS: Y = k(Ap - br) LM: Y = [(Ms/P) + fr]/h Here, k = 1/[s(1 - t) + t + nx]. Let Ap = Ca - Ta + Ip + G + NXa,...

Q:

Forey, Inc., competes against many other firms in a highly competitive industry. Over the last decade, several firms have entered this industry and, as a consequence, Forey is earning a return on...

Q:

3. Why is the stack called a LIFO structure?

Q:

A recent annual report for Sears, Roebuck and Co. disclosed that the company paid preferred dividends in the amount of $1 19.9 million. It declared and paid dividends on common stock in the amount of...

Q:

When the population has a normal distribution, the estimator is sometimes used to estimate the population standard deviation. This estimator is more robust to outliers than the usual sample standard...

Q:

Censored Data a common problem in industry is life testing of components and systems. In this problem, we will assume that lifetime has an exponential distribution with parameter λ, so is an...

Q:

Modify the program Coin Tosses to toss coin n times and print out after every 100 tosses the proportion of heads minus 1/2. Do these numbers appear to approach 0 as n increases? Modify the program...

Q:

Write a line of Java code that will declare a boolean variable named id that is initialized to the value true.

Q:

9. Who developed the Linux operating system ? Why do you think it has been so successful ?

Q:

Assets and sources of funds for depository institutions in the US , UK and The Bahamas