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Chapter 2: Q13P (page 52)

First simplify each of the following numbers to thex+iy form or to the form. Then plot the number in the complex plane. 5(cos2π5+isin2π5)

.

Short Answer

Expert verified

The complex number becomes .5e2π5i

Step by step solution

01

Given Information  

The complex number is.5(cos2π5+sin2π5)

02

Definition of the Complex number

A complex number is a number that is made up of both real and imaginary numbers.

03

Find the value 

The complex number is.5(cos2π5+sin2π5)

z=r(cosθ+sinθ)r=5θ=2π5

The complex number in the form ofreiθis,

z=reiθ=5e2π5i

Hence, the complex number becomes .5e2π5i

The graph is mentioned below.

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Most popular questions from this chapter

Express the following complex numbers in the 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.

19. (1−i)8

Express the following complex numbers in the x+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.

16.(i−3)(1+i3)

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.

7.3e2(1+iπ)

Express the following complex numbers in the x+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.

9.2e-iπ/2

Solve for all possible values of the real numbers xand yin the following equations.

x+iy=3i-ix
See all solutions

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