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Chapter 2: Q6MP (page 80)

Find one or more values of each of the following complex expressions and compare with acomputer solution.

(-e)xi

Short Answer

Expert verified

The value of -exiis -e-x2±2ηπ2 where n = o,1,2,3,.....

Step by step solution

01

Given Information.

The given complex number is -eπi.

02

Definition of Complex Number.

The numbers that are presented in the form of x+iywhere, 'x' is real numbers and 'iy' is an imaginary number, those numbers are referred to as called Complex numbers.

03

Find the value of (-eπi).

Let,

u=-eiπz=In-eu=-eiπ=eIn-eiπ=eiπIn-e.......1

z=In-e=iπ±2nπ=iπ±2nπ.....2n=0,1,2,3,.....

Put the value of equation (2) in equation (1).

u=eiπ±2nπiπ=e-π2±2nπ2n=0,1,2,3,.....

Hence, the value of -eπiis -e-π2±2nπ2 where n = 0,1,2,3,.....

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Most popular questions from this chapter

Express the following complex numbers in the form. Try to visualize each complex number, using sketches as in the examples if necessary. The first twelve problems you should be able to do in your head (and maybe some of the others—try it!) Doing a problem quickly in your head saves time over using a computer. Remember that the point in doing problems like this is to gain skill in manipulating complex expressions, so a good study method is to do the problems by hand and use a computer to check your answers.

3.9e3iπ12

Use Problems 27 and 28 to find the following absolute values. If you understand Problems 27 and 28 and equation (5.1), you should be able to do these in your head.

|eiπ1+i|

Question:First simplify each of the following numbers to the x+iyform or to thereiθform. Then plot the number in the complex plane.

17-12i.

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,θin 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.

role="math" localid="1658476746206" (cos3π2+isin3π2)

Express the following complex numbers in thex+iy form. Try to visualize each complex number, using sketches as in the examples if necessary. The first twelve problems you should be able to do in your head (and maybe some of the others—try it!) Doing a problem quickly in your head saves time over using a computer. Remember that the point in doing problems like this is to gain skill in manipulating complex expressions, so a good study method is to do the problems by hand and use a computer to check your answers.

4. e(1/3)(3+4πi)
See all solutions

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