Real Number System Quiz

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Which of the following statements about rational numbers is correct?

  • All positive integers are rational numbers. (correct)
  • Zero is not considered a rational number.
  • All integers are irrational.
  • Irrational numbers can be expressed as fractions.

Which of the following numbers is classified as an irrational number?

  • √4
  • π (correct)
  • -3
  • 7

What is the value of i to the power of 5 (i⁵)?

  • -1
  • -i
  • i (correct)
  • 1

Which of the following is not a characteristic of integers?

<p>Includes fractions. (C)</p> Signup and view all the answers

Which expression represents the imaginary unit i?

<p>i = √-1 (D)</p> Signup and view all the answers

Flashcards are hidden until you start studying

Study Notes

Real Number System

  • Real numbers comprise both rational and irrational numbers.

Rational Numbers

  • Include all integers, which are natural numbers, their negatives, and zero (e.g., -3, 0, 1, 2).
  • Natural numbers function as counting numbers, beginning from 1 (e.g., 1, 2, 3).

Irrational Numbers

  • Do not represent as fractions and cannot be expressed as the ratio of integers.
  • Examples include the square root of 2 (√2) and π (approximately 3.1416).

Imaginary Numbers

  • Represent numbers that can be expressed using the imaginary unit (i).
  • Defined as i = √-1; provides a basis for complex numbers.
  • i² is calculated as (√-1)², resulting in -1.
  • Higher powers of i follow this pattern:
    • i³ = i² * i = -1 * i = -i
    • i⁴ = i³ * i = -i * i = -i² = 1

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

More Like This

Use Quizgecko on...
Browser
Browser