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Chapter 2: Q8P (page 52)

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

1.6-2.7i .

Short Answer

Expert verified

The complex number becomes 3.138e-1.035i.

The graph is mentioned below:

Step by step solution

01

Given Information

Thecomplex number is 1.6-2.7i .

02

Definition of the Complex number.

A complex number is a number that has real and imaginary numbers and is written in the form as:

z = a + ibwhere a and b are real, and z is the complex number.

03

Find the values

The complex number is 1.6-2.7i .

Find x and y:

x=1.6y=-2.7

Find the value of r :

r=x2+y2r=1.62+2.72=3.138

Find the value of θ:

θ=cos-1xrθ=cos-11.63.138=-1.035z=3.138e-1.035i

The complex number becomes 3.138e-1.035i.

The graph is mentioned below:

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Most popular questions from this chapter

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

x+iy=y+ix

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

10.5(cos40°+isin40°.

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)

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.

253+4i.

Question: Find vand a if z=cos2t+isin2t, can you describe the motion.
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