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Chapter 2: Q57 P (page 54)

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

Re(z2)=4.

Short Answer

Expert verified

This is an equation of a hyperbola.

Step by step solution

01

Given Information

The equation is Re(z2)=4.

02

Definition of the Complex number

A complex number can be represented as:

z=x+iy

Where z is the complex number, x and y are real numbers, and i is known as iota, whose value is -1.

The modulus of a complex number can be calculated as:

|z|=x2+y2

03

Find the value

The equation is Re(z2)=4.

The complex number is z=x+yi.

role="math" localid="1658469578164" z2=(x+yi)2z2=x2-y2+2xyiRez2=4x2-y2=4

Hence, this is an equation of a hyperbola.

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Most popular questions from this chapter

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

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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—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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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.

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