Chapter 2: Q16P (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.
$\frac{1}{0.5 (c o s 40 ° + i s i n 40 °}$ .

Short Answer

Expert verified

The complex number can be written as z = 1.53 - 1.28i .

The graph is shown below as:

Step by step solution

Given Information

The complex number is $\frac{1}{0.5 (\cos 40 ° + i \sin 40 °}$ .

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

Find the values

The complex number is .

$\frac{1}{0.5 (\cos 40 ° + i \sin 40 °}$

Factorize the complex number as:

$0.5 (\cos (40 °) + i \sin (40 °)) = 0.5 e^{i (2 π / 9)} \frac{1}{0.5 (\cos (40 °) + i \sin (40 °))} = \frac{1}{0.5 e^{i (2 π / 9)}} = 2 e^{i (2 π / 9)}$

The value of r and $θ$ are given below:

localid="1658486574125" $θ = - 40 ° = - \frac{2 π}{9} r = 2$

The formulas for x and y are given below:

localid="1658486578027" $x = r \cos (θ) y = r \sin (θ)$

Find x and y

localid="1658486580877" $x = 2 \cos (- 40 °) = 1.53 y = 2 \sin (- 40 °) = - 1.28 z = 1.53 - 0.28 i$

The complex number becomes localid="1658486595837" $z = 1.53 - 0.28 i$ .

The graph is shown 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.
$\frac{1}{0.5 (c o s 40 ° + i s i n 40 °}$ .

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.10.5(cos40°+isin40°.

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

Force

Torque and Rotational Motion

Magnetism and Electromagnetic Induction

Mechanics and Materials

Particle Model of Matter

Work Energy and Power

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.
$\frac{1}{0.5 (c o s 40 ° + i s i n 40 °}$ .