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Chapter 2: Q46P (page 54)

Solve for all possible values of the real numbers xand y in the following equations x+iyx-iy=-i.

Short Answer

Expert verified

The answer is x=-y.

Step by step solution

01

Given information

It is given thatx+iyx-iy=-i .

02

Definition of a complex number

Every complex number can be described 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:

x+iyx-iy=-ix+iy=-ix-iyx+iy=-ix-iy

04

 Step 4: Equate like terms

Equate like terms from both sides:

x+y+x+yi=0+0ix+y=0x+y=0x=-y

Thus, the answer is x=-y.

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Most popular questions from this chapter

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

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Solve for all possible values of the real numbers xand yin the following equations.

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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.

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See all solutions

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