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Chapter 2: Q16 MP (page 80)

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

Short Answer

Expert verified

The set of points are -∞<y<-2.

Step by step solution

01

Given Information

The given relation is Reeiπ/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, Reeiπ/2z>2.

Write eiπ/2in polar form.

eiπ/2=cosπ/2+isinπ/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 -∞<y<-2.

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Most popular questions from this chapter

Find the absolute value of each of the following using the discussion above. Try to do simple problems like these in your head-it saves time.

(1+i1-i)5

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,θ 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.

Show from the power series (8.1) that ddzez=ez.

Find the absolute value of each of the following using the discussion above. Try to do simple problems like these in your head-it saves time.

5-2i5+2i.

Solve for all possible values of the real numbersand in the following equations.

2ix+3=y-i
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