Chapter 9: Q. 43 (page 592)

Write the expression in the standard form $a + i b$ .
role="math" localid="1646666471780" ${[2 (\cos \frac{π}{10} + i \sin \frac{π}{10})]}^{5}$

Short Answer

Expert verified

The expression in the standard form is $32 i$ .

Step by step solution

Step 1. Given information.

Consider the given question,

${[2 (\cos \frac{π}{10} + i \sin \frac{π}{10})]}^{5}$

We know that for a complex number raise to n when it is in the polar form $z^{n} = r^{n} (\cos θ + i \sin (n θ)) . . . . . . (i)$

Write the expression in the standard form $z = (a + b i)$ ,

$x^{5} = {[2 (\cos \frac{π}{10} + i \sin \frac{π}{10})]}^{5}$

Step 2. Use equation (i) and solve the equation.

Using the equation (i),

$x^{5} = 2^{5} [\cos (5 \cdot \frac{π}{10}) + i \sin (5 \cdot \frac{π}{10})] x^{5} = 32 (\cos \frac{π}{2} + i \sin \frac{π}{2}) x^{5} = 32 (0 + i) x^{5} = 32 i$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Write the expression in the standard form $a + i b$ .
role="math" localid="1646666471780" ${[2 (\cos \frac{π}{10} + i \sin \frac{π}{10})]}^{5}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use equation (i) and solve the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Write the expression in the standard form a+ib.role="math" localid="1646666471780" 2cosπ10+isinπ105

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use equation (i) and solve the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Write the expression in the standard form $a + i b$ .
role="math" localid="1646666471780" ${[2 (\cos \frac{π}{10} + i \sin \frac{π}{10})]}^{5}$