\((1+i)^{2}\div i(2i-1)\)
\((1+i)^{2}\div i(2i-1)\)
a
b
The Correct Option is A
Solution and Explanation
solution
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Concepts Used:
Acids and Bases
$P = - \frac{xx^T}{x^Tx}$Acid is any hydrogen-containing substance that is capable of donating a proton (hydrogen ion) to another substance. Base is an ion or molecule capable of accepting a hydrogen ion from acid.
Physical Properties of Acids and Bases
| Physical Properties | ACIDS | BASES |
| Taste | Sour | Bitter |
| Colour on Litmus paper | Turns blue litmus red | Turns red litmus blue |
| Ions produced on dissociation | H+ | OH- |
| pH | <7 (less than 7) | >7 (more than 7) |
| Strong acids | HCl, HNO3, H2SO4 | NaOH, KOH |
| Weak Acids | CH3COOH, H3PO4, H2CO3 | NH4OH |
Chemical Properties of Acids and Bases
| Type of Reaction | Acid | Bases |
| Reaction with Metals | Acid + Metal → Salt + Hydrogen gas (H2) E.g., Zn(s)+ dil. H2SO4 → ZnSO4 (Zinc Sulphate) + H2 | Base + Metal → Salt + Hydrogen gas (H2) E.g., 2NaOH +Zn → Na2ZnO2 (Sodium zincate) + H2 |
| Reaction with hydrogen carbonates (bicarbonate) and carbonates | Metal carbonate/Metal hydrogen carbonate + Acid → Salt + Carbon dioxide + Water E.g., HCl+NaOH → NaCl+ H2O 2. Na2CO3+ 2 HCl(aq) →2NaCl(aq)+ H2O(l) + CO2(g) 3. Na2CO3+ 2H2SO4(aq) →2Na2SO4(aq)+ H2O(l) + CO2(g) 4. NaHCO3+ HCl → NaCl+ H2O+ CO2 | Base+ Carbonate/ bicarbonate → No reaction |
| Neutralisation Reaction | Base + Acid → Salt + Water E.g., NaOH(aq) + HCl(aq) → NaCl(aq) + H2O(l) | Base + Acid → Salt + Water E.g., CaO+ HCl (l) → CaCl2 (aq)+ H2O (l) |
| Reaction with Oxides | Metal oxide + Acid → Salt + Water E.g., CaO+ HCl (l) → CaCl2 (aq)+ H2O (l) | Non- Metallic oxide + Base → Salt + Water E.g., Ca(OH)2+ CO2 → CaCO3+ H2O |
| Dissolution in Water | Acid gives H+ ions in water. E.g., HCl → H+ + Cl- HCl + H2O → H3O+ + Cl– | Base gives OH- ions in water. |
Read more on Acids, Bases and Salts
Formulas Used:
Algebra
Algebraic Identities
- (a + b)2 = a2 + 2ab + b2
- (a - b)2 = a2 - 2ab + b2
- (a + b)(a - b) = a2 - b2
- (x + a)(x + b) = x2 + x(a + b) + ab
Let us look at the algebraic identity: (a + b)2 = a2 + 2ab + b2, and try to understand this identity in algebra and also in geometry. As a proof of this formula, let us try to multiply algebrically the expression and try to find the formula. (a + b)2 = (a + b) × (a + b) = a(a + b) + b(a + b) = a2 + ab + ab + b2. This expression can be geometrically understood as the area of the four sub figures of the below given square diagram. Further, we can consolidate the proof of the identity (a + b)2= a2 + 2ab + b2.
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