REAL AND COMPLEX NUMBERS

Mathematics Saima Khan January 28, 2024 0 Comments

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 ( $i^{2} = - 1$ ).

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.

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., $5 + 0 i$ ).

Q4: How do you add two complex numbers?

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