Podcast
Play an AI-generated podcast conversation about this lesson
Questions and Answers
Which of the following statements about rational numbers is correct?
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?
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)?
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?
Which of the following is not a characteristic of integers?
Signup and view all the answers
Which expression represents the imaginary unit i?
Which expression represents the imaginary unit i?
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.
