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Chapter 2: Q16 MP (page 80)

Describe the set of points zfor which Re(ei蟺/2z)>2.

Short Answer

Expert verified

The set of points are -鈭�<y<-2.

Step by step solution

01

Given Information

The given relation is Reei蟺/2>2.

02

Definition of Complex Numbers

The numbers that are presented in the form of x+iywhere, 'x'is real numbers and 'iy' is an imaginary number, those numbers are referred to as called Complex numbers.

03

 Find the ratio of the series.

The given relation is, Reei蟺/2z>2.

Write ei蟺/2in polar form.

ei蟺/2=cos蟺/2+isin蟺/2=i

Letz=x=yi

Find Rezi>2, the real part of the complex number.

Rezi=Reix+yi=Rexi-y=-y-y>2

Or y<-2 .

So, the set of points are -鈭�<y<-2.

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Most popular questions from this chapter

Solve for all possible values of the real numbers x and y in the following equations.

x+iy=3i-4

Find and ifz=(1-it)2t+i .

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

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.

Test each of the following series for convergence.

鈭�1+in2
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