REAL AND COMPLEX NUMBERS

Short Questions and Answers:

Q1: What is a real number?

Ans1: Real numbers encompass all rational and irrational numbers, including integers, fractions, decimals, and square roots of non-negative numbers.

Q2: Define a complex number.

Ans2: A complex number takes the form $a+bi$, where both ‘a’ and ‘b’ are real numbers, and ‘i’ represents the imaginary unit (i2=−1).

Q3: Can the square root of a negative number be a real number?

Ans3: No, the square root of a negative number is not a real number. Instead, it results in an imaginary number.

Q4: What is the conjugate of a complex number $a+bi$?

Ans4: The conjugate is $a-bi$. This means you simply change the sign of the imaginary part.

Q5: How do you represent real numbers on the number line?

Ans5: You can position real numbers on the number line, which extends infinitely in both directions with integers at regular intervals.

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Mathematics I

REAL AND COMPLEX NUMBERS

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Category: Real and Complex Numbers

1. Non-terminating decimal fraction is also known as

quadratic fraction

linear fraction

terminating decimal fraction

recurring decimal fraction

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Category: Real and Complex Numbers

2. The decimal form of 5 ⁄ 8 is

0.578

1.324

0.313

0.625

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Category: Real and Complex Numbers

3. The set of real numbers is denoted by

R

Q

Q'

R'

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Category: Real and Complex Numbers

4. √3 is the example of

irrational numbers

odd numbers

rational numbers

integers

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Category: Real and Complex Numbers

5. Add 2 + 3i  and - 3 + 5i is

3 + 2i

-1 - 8i

5 + 3i

-1 + 8i

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Category: Real and Complex Numbers

6. π is a

irrational number

whole number

natural number

rational number

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7. The decimal fraction in which some digits are repeated again and again in same order in its decimal part is called

quadratic fraction

terminating decimal fraction

non-terminating decimal fraction

linear fraction

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Category: Real and Complex Numbers

8. The set of irrational numbers is denoted by

Q'

R'

Q

R

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Category: Real and Complex Numbers

9. The numbers in the form of p ⁄ q where p, q are integers and q is not zero are called

whole numbers

rational numbers

irrational numbers

prime numbers

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Category: Real and Complex Numbers

10. 4 ⁄ 11 = 0.2222 is the example of

terminating decimal fraction

quadratic fraction

non-terminating decimal fraction

linear fraction

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Category: Real and Complex Numbers

11. The union of the set of rational and irrational numbers is known as

set of irrational numbers

set of prime numbers

set of rational numbers

set of real numbers

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Category: Real and Complex Numbers

12. The numbers 1, 2, 3, .... which are used for counting certain objects are called

odd numbers

whole numbers

prime numbers

natural numbers

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Category: Real and Complex Numbers

13. The set consist of positive integers, zero and negative integers is called

set of irrational numbers

set of integers

set of prime numbers

set of even numbers

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Category: Real and Complex Numbers

14. 2 ⁄ 10 = 0.2 is the example of

non-terminating decimal fraction

linear fraction

quadratic fraction

terminating decimal fraction

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Category: Real and Complex Numbers

15. The numbers which can be expressed as quotient of integers are known as

prime numbers

rational numbers

irrational numbers

whole numbers

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FAQ: Frequently Asked Questions

Q1: Are all integers real numbers?

Ans: Yes, all integers are a subset of real numbers. Specifically, they include positive and negative whole numbers, including zero.

Q2: What is the difference between a real and an imaginary number?

Ans: Real numbers are those that appear on the number line, whereas imaginary numbers involve the imaginary unit ‘i’ and are expressed as a multiple of ‘i’.

Q3: Can a real number also be a complex number?

Ans: Yes, every real number can also be a complex number with an imaginary part of zero (e.g., $5+0i$).

Q4: How do you add two complex numbers?

Ans: To add two complex numbers, like $a+bi$ and $c+di$, you first add their real parts ($a$ and $c$). Then, you add their imaginary parts ($b$ and $d$) separately.