Questions and Answers
Which of the following statements about rational numbers is correct?
Which of the following numbers is classified as an irrational number?
What is the value of i to the power of 5 (i⁵)?
Which of the following is not a characteristic of integers?
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Which expression represents the imaginary unit i?
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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
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Description
Test your knowledge of the real number system, exploring both rational and irrational numbers. Dive into integers, natural numbers, and even imaginary numbers like the square root of negative one. This quiz will help solidify your understanding of these fundamental concepts in mathematics.
