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Chapter 2: Q15P (page 52)

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

5-2i5+2i.

Short Answer

Expert verified

The complex number can be written z=e-43.6i.

The graph is mentioned below:

Step by step solution

01

Given Information

5-2i5+2iThe complex number is .

02

Definition of the Complex number

Real and imaginary numbers combine and form a complex number as:

z = a + ibHere a and b are the real numbers, and z is a complex number

03

Find the values

The complex number is 5-2i5+2i.

Rationalize the complex number as:

z=5-2i5+2i×5-2i5-2i=25-20i+4i225-4i2=21-20i29=2129-2029i

Find x and y.

x=2129y=-2029

Find the value of r.

r=x2+y2r=441841+400841=1

Find the value of .

θ=sin-1yrθ=sin-1-2029=-43.6°

The complex number can be written as z=e-43.6°i.

The graph is mentioned below as:

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Most popular questions from this chapter

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.

23. (1+i)48(3−i)25

Test each of the following series for convergence.

∑(2+i3-4i)2n

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.

10.role="math" localid="1653071800850" eiπ+e-iπ

Find the power series for excosxand for exsinxfrom the series for ezin the following way: Write the series for ez; put z=x+iy. Show that ez=ex(cosy+isiny); take real and imaginary parts of the equation, and put y=x.


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.

22.1−i242
See all solutions

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