Doubtly
@Doubtly · Joined Feb 2021
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- The Extract deals with the atmosphere of two homes. Collect the words associated with – Home Library Garden Home: old, brown, bare, shabby, stately stone mansion, comfort, luxury, big coach house, lovely things, rich curtains, lifeless, lawn, encha... 1
- Find proverbs, maxims and idioms related to ‘friendship’. Birds of a feather flock together. A friend in need is a friend in deed. Friendship is love with understanding. To get on like a house on fi... 1
- Give a brief account of the interaction between Grandpa and Jo. Grandpa and Jo had an interesting interaction as Jo had come out of her initial fear after having a closer look at him. Grandpa had overhear... 1
- Write down in your own words the way Laurie confirmed the names of the March sisters. The March family sometimes forgot to put the curtain down at the window and that helped Laurie, their neighbor, to observe minutely inside t... 1
- Bring out the contrast between the two houses with the help of the following points: House of March House of Laurence 1. Old, brown house 2. Rather bare and shabby 3. Children played all around 4. A lively household having fo... 1
- Jo’s decision to make friends with the lonely boy next door proves to be a good one. Elaborate. Jo was bold, friendly and warm person who observed the boy next door closely and came to the conclusion that he was hungry for friends and f... 1
- z – z¯ = 6i ( z – z¯ = 6i) z – z¯ = (2 + 3i) – (2 – 3i) = 2 + 3i – 2 + 3i = 6i 1
- (1 + 2i) 2 (1 – i) Let z = (1 + 2i)² (1 – i) = (1 + 4i + 4i²) (1 – i) = [1 + 4i + 4(-1)] (1 – i) ….[∵ i² = -1] = (-3 + 4i) (1 – i) = -3 + 3i + 4i – 4i² = -3 +... 1
- (1 + ω)(1 + ω2)(1 + ω4)(1 + ω8) ω is the complex cube root of unity. ω³ = 1 and 1 + ω + ω² = 0 Also, 1 + ω² = -ω, 1 + ω = -ω² and ω + ω² = -1 (1 + ω)(1 + ω²)(1 + ω⁴)(1 + ω⁸... 1
- (1 – ω – ω2)3 + (1 – ω + ω2)3 ω is the complex cube root of unity. ω³ = 1 and 1 + ω + ω² = 0 Also, 1 + ω² = -ω, 1 + ω = -ω² and ω + ω² = -1 (1 – ω – ω²)³ + (1 – ω + ω²)³... 1
- (1 + ω – ω2) 6 = 64 Proof: since 1 + ω = -ω² , the expression becomes (-2ω²)⁶ = 64 . Here ω is a complex cube root of unity, so ω³ = 1 and 1 + ω + ω² = 0 , whic... 1
- If ω is the complex cube root of unity, show that (i) (2 – ω)(2 – ω2) = 7 ω is the complex cube root of unity. ω³ = 1 and 1 + ω + ω² = 0 Also, 1 + ω² = -ω, 1 + ω = -ω² and ω + ω² = -1 L.H.S. = (2 – ω)(2 – ω²) = 4 –... 1
- If ω is a complex cube root of unity, prove that (1 – ω + ω2)6 + (1 + ω – ω2)6 = 128. ω is the complex cube root of unity. ∴ ω³ = 1 and 1 + ω + ω² = 0 Also, 1 + ω² = -ω, 1 + ω = -ω² ∴ L.H.S. = (1 – ω + ω²)⁶ + (1 + ω – ω²)⁶ = [... 1
- 18i complex number Let √18i = a + bi, where a, b ∈ R. Squaring on both sides, we get 18i = a² + b² i² + 2abi 0 + 18i = a² – b² + 2abi …..[∵ i² = -1] Equating r... 1
- i131 + i49 complex number i¹³¹ + i⁴⁹ = (i⁴)³² . i³ + (i⁴)¹² . i = (1)³² (-i) + (1)¹² . i = -i + i = 0 2
- 2x + i9 y(2 + i) = x i7 + 10 i16 2x + i⁹ y(2 + i) = x i⁷ + 10 i¹⁶ 2x + (i⁴)² . i . y(2 + i) = x(i²)³ . i + 10 . (i⁴)⁴ 2x + (1)² . iy(2 + i) = x(-1)³ . i + 10(1)⁴ ……..[∵ i² =... 1
- A 0.1 m solution of K2SO4 in water has a freezing point of – 4.3 °C. Given: Molality of K₂SO₄ solution = m = 0.1 m Freezing point of solution = T_f = – 4.3 °C K_f of water = 1.86 K kg mol^(–1)To find: van’t Ho... 1
- Write the equation relating boiling point elevation to the concentration of the solution. The boiling point elevation is directly proportional to the molality of the solution. Thus, Δ Tb ∝ m ∴ Δ Tb ∝ Kb m where, m is the molality... 1