Chapter 2: Q17P (page 52)

Question:First simplify each of the following numbers to the x+iyform or to the $r e^{i θ}$ form. Then plot the number in the complex plane.
${(1.7 - 3.2 i)}^{2}$ .

Short Answer

Expert verified

The complex number can be written as: $z = 13.13 e^{- 2.16 i}$

The graph is mentioned below:

Step by step solution

Given Information

The complex number is ${(1.7 - 3.2 i)}^{2}$ .

Definition of the Complex number

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

$z = a + i b$ Here a and b are the real numbers, and z is a complex number

Find the values

The complex number is ${(1.7 - 3.2 i)}^{2}$ .

Factorize the complex number.

$z = {(1.7 - 3.2 i)}^{2} = {(1.7)}^{2} - 2 \times 1.7 \times 3.2 i + {(3.2 i)}^{2} z = 2.89 - 10.24 - 1.88 i z = - 7.35 - 10.88 i$

Find x and y:

$z = - 7.35 - 10.88 i x = - 7.35 y = - 10.88$

Find the value of r :

$r = \sqrt{x^{2} + y^{2}} r = \sqrt{{(- 7.35)}^{2} + {(- 10.88)}^{2}} = 13.13$

Find the value of $θ$ :

localid="1658488071069" $θ = \cos^{- 1} (\frac{x}{r}) θ = \cos^{- 1} (- \frac{7.35}{13.13}) = - 124 ° = - 2.16 rad z = 13.13 e^{- 2.16 i}$

The complex number can be written as:localid="1658488077050" $z = 13.13 e^{- 2.16 i}$

The graph is mentioned below:

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Question:First simplify each of the following numbers to the x+iyform or to the $r e^{i θ}$ form. Then plot the number in the complex plane.
${(1.7 - 3.2 i)}^{2}$ .

Short Answer

Step by step solution

Given Information

Definition of the Complex number

Find the values

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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.(1.7-3.2i)2 .

Short Answer

Step by step solution

Given Information

Definition of the Complex number

Find the values

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electrostatics

Energy Physics

Oscillations

Physical Quantities And Units

Measurements

Famous Physicists

Study anywhere. Anytime. Across all devices.

Question:First simplify each of the following numbers to the x+iyform or to the $r e^{i θ}$ form. Then plot the number in the complex plane.
${(1.7 - 3.2 i)}^{2}$ .