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Chapter 2: Q52P (page 54)

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

Rez=0.

Short Answer

Expert verified

The equation is the imaginary axis (y-axis).

Step by step solution

01

Given Information

The equation is Rez=0.

02

Definition of the Complex number

A complex number can be written as:

z=x+iy

Where z is the complex number, x and y are real numbers, 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 isRez=0 .

Rez=0x=0

Hence, the equation is the imaginary axis (y-axis).

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Most popular questions from this chapter

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.

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.

3ei2x.

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

Find the disk on convergence for each of the following complex power series.

鈭�n-0m(z-2+i)n2n

For each of the following numbers, first visualize where it is in the complex plane. With a little practice you can quickly findx,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(cos蟺6+isin蟺6).
See all solutions

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