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Chapter 2: Q43P (page 54)

Solve for all possible values of the real numbersand in the following equations (x-iy)2=2ix.

Short Answer

Expert verified

The answer is x,y=0,0or1,1or-1,1.

Step by step solution

01

Given information

It is given thatx-iy2=2ix. .

02

Definition of a complex number

Every complex number can be described as:

z=a+bi

Where aand bare 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:

x-iy2=2ixx2+2xyi-y2=2xi

04

Equate like terms

Equate like terms from both sides:

x2-y2=0x2=y2andxy-1=0

05

Evaluate possible solutions

The above equation implies:

Ifx=0theny=0Ify=1thenx=卤1

Thus, the final answer is x,y=0,0or1,1or-1,1.

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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.

3.

Find each of the following in rectangular a+zb form if z=2-3t; if z=x+yz.

1+z1-z.

Find each of the following in rectangular a+bz form ifz=2if ; if z=x+yz .

role="math" localid="1658486330935" 1z+1.

Question: Describe geometrically the set of points in the complex plane satisfying the following equations. .

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.

2-2i.

See all solutions

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