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Complex Numbers and Quadratic Equations Practice Questions

Class 11 · Mathematics · 1122 free MCQs with instant results and detailed explanations.

1122
Total
415
Easy
529
Medium
178
Hard

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Topics in Complex Numbers and Quadratic Equations

Complex Numbers 328
Algebra of Complex Numbers 298
Quadratic Equations 181
Modulus and Argument 315

Sample Questions from Complex Numbers and Quadratic Equations

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What is the modulus of the complex number 3 + 4i?
A. 5
B. 7
C. 6
D. 4
Show Answer & Explanation
Correct Answer: A
The modulus is calculated using √(a² + b²) where a is the real part and b is the imaginary part.
Q2
Easy
Which of the following is an example of a purely imaginary number?
A. 5
B. 3 + 0i
C. 0 + 4i
D. 2 - 2i
Show Answer & Explanation
Correct Answer: C
A purely imaginary number has no real part, only an imaginary part.
Q3
Easy
If z = 1 + i, what is the value of z^2?
A. 2i
B. 1 + 2i - 1
C. 2 + 2i
D. 0
Show Answer & Explanation
Correct Answer: C
To find z^2, expand (1 + i)(1 + i) using the distributive property.
Q4
Medium
What is the modulus of the complex number z = 3 - 4i?
A. 5
B. 7
C. 6
D. 4
Show Answer & Explanation
Correct Answer: A
The modulus of a complex number z = a + bi is given by √(a² + b²). Here, |z| = √(3² + (-4)²) = √(9 + 16) = √25 = 5.
Q5
Medium
Which of the following represents the complex conjugate of z = 5 + 3i?
A. 5 - 3i
B. 3 - 5i
C. -5 - 3i
D. 5 + 3i
Show Answer & Explanation
Correct Answer: A
The complex conjugate of a complex number z = a + bi is given by a - bi. Here, the conjugate is 5 - 3i.
Q6
Medium
If z = 3 + 4i, what is the real part of z?
A. 3
B. 4
C. 7
D. 0
Show Answer & Explanation
Correct Answer: A
In the complex number z = a + bi, the real part is 'a'. Here, the real part is 3.
Q7
Medium
Find the value of i^10.
A. 1
B. i
C. -1
D. -i
Show Answer & Explanation
Correct Answer: A
The powers of i cycle through 1, i, -1, -i. Since 10 mod 4 = 2, i^10 = (i^2)^5 = (-1)^5 = -1.
Q8
Hard
If z = 3 + 4i, what is the modulus of z?
A. 5
B. 7
C. 8
D. 12
Show Answer & Explanation
Correct Answer: A
The modulus is calculated as √(3² + 4²) = √(9 + 16) = √25 = 5.
Q9
Hard
If z = 2 + 3i, find the conjugate of z.
A. 2 - 3i
B. -2 + 3i
C. -2 - 3i
D. 3 + 2i
Show Answer & Explanation
Correct Answer: A
The conjugate of z = a + bi is defined as a - bi, so the conjugate is 2 - 3i.
Q10
Hard
Which of the following is a pure imaginary number?
A. 5 + 0i
B. 0 - 2i
C. 3 + 4i
D. 2
Show Answer & Explanation
Correct Answer: B
A pure imaginary number has no real part. 0 - 2i fits this definition.

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Complex Numbers and Quadratic Equations — Class 11 Mathematics Practice Questions Online

This page contains 1122 practice MCQs for the chapter Complex Numbers and Quadratic Equations in Class 11 Mathematics. The questions are organized by difficulty — 415 easy, 529 medium, 178 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 4 topics, giving you comprehensive coverage of the entire chapter.