Complex Numbers and Quadratic Equations — Class 11 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Complex Numbers and Quadratic Equations" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Complex Numbers and Quadratic Equations" — 8 important questions with detailed ans…
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Key Questions Covered:
- Express (3 + 2i) + (1 - 4i) and (3 + 2i) - (1 - 4i) in the form a + bi.
- Multiply (2 + 3i)(1 - i) and express the result in the form a + bi.
- Find the complex conjugate and modulus of z = 3 - 4i. Also find z · z̄.
- + 5 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Express (3 + 2i) + (1 - 4i) and (3 + 2i) - (1 - 4i) in th… | ✓ Solved |
| Multiply (2 + 3i)(1 - i) and express the result in the fo… | ✓ Solved |
| Find the complex conjugate and modulus of z = 3 - 4i. Als… | ✓ Solved |
Showing 3 of 8 questions
Q1: Express (3 + 2i) + (1 - 4i) and (3 + 2i) - (1 - 4i) in the form a + bi.
Step 1: Add the complex numbers.
(3 + 2i) + (1 - 4i)
= 3 + 1 + 2i - 4i
= 4 + (2 - 4)i
= 4 - 2i
Step 2: Subtract the complex numbers.
(3 + 2i) - (1 - 4i)
= 3 - 1 + 2i - (-4i)
= 2 + 2i + 4i
= 2 + 6i
Step 3: Verify using the general rule.
For addition: (a + bi) + (c + di) = (a + c) + (b + d)i
For sub...
Q2: Multiply (2 + 3i)(1 - i) and express the result in the form a + bi.
Step 1: Use the distributive property (FOIL).
(2 + 3i)(1 - i)
= 2(1) + 2(-i) + 3i(1) + 3i(-i)
= 2 - 2i + 3i - 3i²
Step 2: Use i² = -1.
= 2 - 2i + 3i - 3(-1)
= 2 - 2i + 3i + 3
= (2 + 3) + (-2 + 3)i
= 5 + i
Step 3: Verify by expanding carefully.
(2 + 3i)(1 - i) = 2·1 + 2·(-i) + 3i·1 + 3i·(-i)
= 2 - ...
Q3: Find the complex conjugate and modulus of z = 3 - 4i. Also find z · z̄.
Step 1: Find the complex conjugate z̄.
If z = 3 - 4i, then z̄ = 3 + 4i
Step 2: Find the modulus |z|.
|z| = √(3² + (-4)²) = √(9 + 16) = √25 = 5
Step 3: Calculate z · z̄.
z · z̄ = (3 - 4i)(3 + 4i)
= 3² - (4i)²
= 9 - 16i²
= 9 - 16(-1)
= 9 + 16
= 25
Step 4: Verify the relationship.
Notice that z · z̄...
Showing 3 of 8 questions. Visit the full page for complete solutions.