Chapter 2: Q7P (page 52)

Question:First simplify each of the following numbers to the x+iyform or to the $r e^{iθ}$ form. Then plot the number in the complex plane.
$(\frac{3 + i}{2 + i})$

Short Answer

Expert verified

The complex number can be written as $\sqrt{2} e^{- i 0.141}$ .

The graph is mentioned below:

Step by step solution

Given Information

Thecomplex number is $(\frac{3 + i}{2 + i})$ .

Definition of the Complex number.

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

$z = a + i b$ where a and b are real, and z is the complex number.

Find the value

Factorize the complex number.

$z = \frac{3 + i}{2 + i} \times \frac{2 - i}{2 - i} = \frac{6 - i - i^{2}}{4 - i^{2}} = \frac{7}{5} - \frac{i}{5}$

Find x and y

$x = \frac{7}{5} = - \frac{1}{5}$

Find the value of r .

$r = \sqrt{x^{2} + y^{2}} r = \sqrt{\frac{49}{25} + \frac{1}{25}} = \sqrt{\frac{50}{25}} = \sqrt{2}$

Find the value of .

$θ = \sin^{- 1} (\frac{y}{r}) θ = \sin^{- 1} (\frac{\frac{1}{5}}{\sqrt{2}}) = - 0.141 (\frac{3 + i}{2 + i}) = \sqrt{2} e^{- i 0.141}$

The complex number can be written as $\sqrt{2} e^{- i 0.141}$ .

The graph is mentioned below as:

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Question:First simplify each of the following numbers to the x+iyform or to the $r e^{iθ}$ form. Then plot the number in the complex plane.
$(\frac{3 + i}{2 + i})$

Short Answer

Step by step solution

Given Information

Definition of the Complex number.

Find the value

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Question:First simplify each of the following numbers to the x+iyform or to thereiθform. Then plot the number in the complex plane.(3+i2+i)

Short Answer

Step by step solution

Given Information

Definition of the Complex number.

Find the value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electromagnetism

Thermodynamics

Solid State Physics

Circular Motion and Gravitation

Conservation of Energy and Momentum

Magnetism

Study anywhere. Anytime. Across all devices.

Question:First simplify each of the following numbers to the x+iyform or to the $r e^{iθ}$ form. Then plot the number in the complex plane.
$(\frac{3 + i}{2 + i})$