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Chapter 2: Q18P (page 76)

Show that tanh z never takes the values卤1.

Short Answer

Expert verified

It has been proved thattanh z never takes the values卤1.

Step by step solution

01

Given Information.

The given expression is tanh z.

02

Meaning of rectangular form.

Represent the complex number in rectangular form means writing the given complex number in the form of x + iy in which x is the real part and y is the imaginary part.

03

Solve the equation.

Solve the given equation tan z = i in the hint.

ez-e-zez+e-z=-1ez-e-z=-ez-e-z2ez=0

Previous equation has no exact solution because ezis zero only at -鈭�.

ez-e-zez+e-z=1ez-e-z=-ez-e-z-2e-z=0

Previous equation has no exact solution because ezis zero only at -鈭�.

The solution of the equation is卤鈭� which is not possible.

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Most popular questions from this chapter

For each of the following numbers, first visualize where it is in the complex plane. With a little practice you can quickly find x,y,r,胃in your head for these simple problems. Then plot the number and label it in five ways as in Figure 3.3. Also plot the complex conjugate of the number.

2i-2.

Find the absolute value of each of the following using the discussion above. Try to do simple problems like these in your head-it saves time.

3ii-3.

Solve for all possible values of the real numbersand in the following equations.

2ix+3=y-i

For each of the following numbers, first visualize where it is in the complex plane. With a little practice you can quickly findx,y,r,胃 in your head for these simple problems. Then plot the number and label it in five ways as in Figure 3.3. Also plot the complex conjugate of the number.

5(cos20掳+isin20掳).

Question: Find vand a if z=cos2t+isin2t, can you describe the motion.
See all solutions

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