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Chapter 2: Q30P (page 64)

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.

|e3-i|

Short Answer

Expert verified

The absolute value of the expression e3-i=e3.

Step by step solution

01

 Step 1: Given information

The given complex number is e3-i.

02

 Step 2: Definition of complex numbers 

The numbers that are presented in the form of a+ib where are real numbers and is an imaginary number called complex numbers.

03

Use the result concluded in problem 27

Let the complex number e3-ibe .

Z=e3e-i 鈥︹��. (1)

Use the result concluded in problem 27.

R=ex+yiR=ex 鈥︹��. (2)

Compare equations (1) and (2) as:

R=e3.

Hence the absolute value of the expression e3-i=e3.

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Most popular questions from this chapter

Express the following complex numbers in the x + 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鈥攖ry 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.

17.1(1+i)3

Question:First simplify each of the following numbers to the x+iy form or to the rei胃form. Then plot the number in the complex plane.

1.6-2.7i .

Express the following complex numbers in the x+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鈥攖ry 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.

21.1鈭�i240

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.

5-2i5+2i.

Solve for all possible values of the real numbers x and y in the following equations.

x+iy=3i-4
See all solutions

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