Complex Numbers and Quadratic Equations
Madhya Pradesh Board · Class 11 · Mathematics
Flashcards for Complex Numbers and Quadratic Equations — Madhya Pradesh Board Class 11 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Solve: x^2 + 1 = 0
Answer
Step 1: Rearrange to x^2 = -1. Step 2: No real number has a negative square. Step 3: Introduce i such that i^2 = -1. Answer: The equation has no real solution; its complex solutions are i and -i.
हल करें: x^2 + 1 = 0
Answer
चरण 1: x^2 = -1 के रूप में पुनर्व्यवस्थित करें। चरण 2: किसी भी वास्तविक संख्या का वर्ग ऋणात्मक नहीं होता है। चरण 3: i को इस प्रकार प्रस्तुत करें कि i^2 = -1 हो। उत्तर: समीकरण का कोई वास्तविक हल नहीं ह…
Solve: 4x + i(3x - y) = 3 + i(-6)
Answer
Step 1: Compare real parts: 4x = 3. Step 2: So x = 3/4. Step 3: Compare imaginary parts: 3x - y = -6. Step 4: Substitute x = 3/4: 9/4 - y = -6. Step 5: So -y = -33/4, hence y = 33/4. Answer: x = 3/4, …
हल करें: 4x + i(3x - y) = 3 + i(-6)
Answer
चरण 1: वास्तविक भागों की तुलना करें: 4x = 3. चरण 2: तो x = 3/4. चरण 3: काल्पनिक भागों की तुलना करें: 3x - y = -6. चरण 4: x = 3/4: 9/4 - y = -6. प्रतिस्थापित करें चरण 5: तो -y = -33/4, इसलिए y = 33/4.
Find the sum: (2 + 3i) + (-6 + 5i)
Answer
Step 1: Add real parts: 2 + (-6) = -4. Step 2: Add imaginary parts: 3i + 5i = 8i. Step 3: Combine the results. Answer: -4 + 8i.
योग ज्ञात कीजिए: (2 + 3i) + (-6 + 5i)
Answer
चरण 1: वास्तविक भाग जोड़ें: 2 + (-6) = -4. चरण 2: काल्पनिक भाग जोड़ें: 3i + 5i = 8i. चरण 3: परिणामों को मिलाएं। उत्तर: -4 + 8i.
Find the difference: (6 + 3i) - (2 - i)
Answer
Step 1: Change subtraction into addition of the negative. Step 2: (6 + 3i) - (2 - i) = (6 + 3i) + (-2 + i). Step 3: Add real parts: 6 + (-2) = 4. Step 4: Add imaginary parts: 3i + i = 4i. Answer: 4 + …
अंतर ज्ञात कीजिए: (6 + 3i) - (2 - i)
Answer
चरण 1: घटाव को ऋणात्मक के जोड़ में बदलें। चरण 2: (6 + 3i) - (2 - i) = (6 + 3i) + (-2 + i). चरण 3: वास्तविक भाग जोड़ें: 6 + (-2) = 4. चरण 4: काल्पनिक भाग जोड़ें: 3i + i = 4i. उत्तर: 4 + 4i.
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