Podcast
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?
Which expression represents the imaginary unit i?
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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