Chapter Exam

Chapter-4 Complex Numbers and Quadratic Equations — Online MCQ Test

Q: What is the value of i²?

Answer: A. -1 — By definition, the imaginary unit i is defined such that i² = -1.

Q: If z = 3 + 4i, what is the real part of z?

Answer: B. 3 — In the complex number z = a + bi, a is the real part and b is the imaginary coefficient; here a = 3.

Q: If z₁ = 2 + 3i and z₂ = 1 - i, find z₁ + z₂.

Answer: A. 3 + 2i — z₁ + z₂ = (2 + 3i) + (1 - i) = (2+1) + (3-1)i = 3 + 2i.

Q: If z = (1 + 2i)/(1 - i), find z in the form a + bi.

Answer: A. -1/2 + 3i/2 — Multiply by conjugate: [(1+2i)(1+i)]/[(1-i)(1+i)] = [1+i+2i-2]/2 = [-1+3i]/2 = -1/2 + 3i/2.

Q: For what value of k does x² - 2x + k = 0 have one real and one imaginary root?

Answer: D. No such k exists — For a quadratic with real coefficients, roots are either both real or both complex conjugates; mixed real and non-real imaginary roots are impossible.

MATHS · CLASS 11 FIRST PUC · Karnataka State Board

Practice Chapter-4 Complex Numbers and Quadratic Equations with a free chapter-wise online MCQ test for Karnataka State Board CLASS 11 FIRST PUC MATHS. This chapter covers: Imaginary unit (i) - Real and imaginary parts - Conjugate - Modulus - Argand plane - Polar representation - Square root of negative numbers - Quadratic formula. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter-4 Complex Numbers and Quadratic Equations — Important Questions & Answers (FAQ)

Frequently asked questions from Karnataka State Board CLASS 11 FIRST PUC MATHS — Chapter-4 Complex Numbers and Quadratic Equations, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is the value of i²?

A. -1 ✓
B. 1
C. i
D. -i

Answer: A. -1
By definition, the imaginary unit i is defined such that i² = -1.

If z = 3 + 4i, what is the real part of z?

A. 4
B. 3 ✓
C. 7
D. 12

Answer: B. 3
In the complex number z = a + bi, a is the real part and b is the imaginary coefficient; here a = 3.

If z₁ = 2 + 3i and z₂ = 1 - i, find z₁ + z₂.

A. 3 + 2i ✓
B. 1 + 4i
C. 3 - 2i
D. 2 + 3i

Answer: A. 3 + 2i
z₁ + z₂ = (2 + 3i) + (1 - i) = (2+1) + (3-1)i = 3 + 2i.

If z = (1 + 2i)/(1 - i), find z in the form a + bi.

A. -1/2 + 3i/2 ✓
B. 1/2 - 3i/2
C. -1 + 3i
D. 1 + 3i

Answer: A. -1/2 + 3i/2
Multiply by conjugate: [(1+2i)(1+i)]/[(1-i)(1+i)] = [1+i+2i-2]/2 = [-1+3i]/2 = -1/2 + 3i/2.

For what value of k does x² - 2x + k = 0 have one real and one imaginary root?

A. k = 1
B. k > 1
C. k = 0
D. No such k exists ✓

Answer: D. No such k exists
For a quadratic with real coefficients, roots are either both real or both complex conjugates; mixed real and non-real imaginary roots are impossible.

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