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Chapter 2: Q36P (page 54)

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

2ix+3=y-i

Short Answer

Expert verified

The answer is obtained as:

x=-12,y=3

Step by step solution

01

Given information

It is given that 2ix+3=y-i.

02

Definition of a complex number

Every complex number can be written as:


z=a+bi

Whereaandbare both real numbers, z is the complex number, and i is known as iota, which makes z a complex number.

03

Begin by stating the given information

State the given information as:

2ix+3=y-i

04

Equate like terms

Equate like terms from both sides as:

2ix+3=y-i2x=-1x=-12andy=3

Thus, the final answer is obtained as:

x=-12.y=3

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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.

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

5-2i5+2i.

Describe geometrically the set of points in the complex plane satisfying the following equations.|z+1|+|z-1|=8.

Express the following complex numbers in the x+iyform. 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.

11. localid="1653075389121" role="math" 2e5i蟺/4

Express the following complex numbers in thex+iyform. 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.

5. e5蟺颈
See all solutions

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