Chapter 2: Q38P (page 64)

Use Problems 27 and 28 to find the following absolute values. If you understand Problems 27 and 28 and equation (5.1), you should be able to do these in your head.
$| \frac{e^{iπ}}{1 + i} |$

Short Answer

Expert verified

The absolute value of the expression $| \frac{e^{i π}}{1 + i} | = \frac{1}{\sqrt{2}}$ .

Step by step solution

Given information

The given complex number is $| \frac{e^{iπ}}{1 + i} |$ .

Definition of complex numbers

If a and b are real numbers, then a combination of these real numbers with the imaginary number i can be represented as:

$z = a + ib$

Here z is the complex number.

Use the result concluded in problem 27

Let the complex number be $|Z| = |\frac{e^{iπ}}{1 + i}|$ .

Use the result concluded in problem 27.

role="math" localid="1658726206626" $|z| = |\frac{z_{1}}{z_{2}}| |\frac{z_{1}}{z_{2}}| = \frac{r_{1}}{r_{2}} \frac{r_{1}}{r_{2}} = R \dots \dots \dots \dots \dots . . (1)$

Find the modulus $r_{1} a n d r_{2}$ .

$r_{1} = 1 r_{2} = \sqrt{1^{2} + 1^{2}} = \sqrt{2}$

Substituting values in equation (1), we get,

$R = \frac{1}{\sqrt{2}}$

Hence the absolute value of the expression $|\frac{e^{i π}}{1 + i}| = \frac{1}{\sqrt{2}}$ .

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Use Problems 27 and 28 to find the following absolute values. If you understand Problems 27 and 28 and equation (5.1), you should be able to do these in your head.
$| \frac{e^{iπ}}{1 + i} |$

Short Answer

Step by step solution

Given information

Definition of complex numbers

Use the result concluded in problem 27

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Use Problems 27 and 28 to find the following absolute values. If you understand Problems 27 and 28 and equation (5.1), you should be able to do these in your head.|eiπ1+i|

Short Answer

Step by step solution

Given information

Definition of complex numbers

Use the result concluded in problem 27

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

Scientific Method Physics

Electric Charge Field and Potential

Mechanics and Materials

Geometrical and Physical Optics

Linear Momentum

Study anywhere. Anytime. Across all devices.

Use Problems 27 and 28 to find the following absolute values. If you understand Problems 27 and 28 and equation (5.1), you should be able to do these in your head.
$| \frac{e^{iπ}}{1 + i} |$