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Exercise 2.6 (Solutions): 18 Hits, Last modified: 3 months ago; e or false. (i) $\sqrt{-3}\cdot\sqrt{-3} = 3$\\ (ii) $i^{73}=-i$\\ (iii) $i^{10} = -1$\\ (iv) Complex... tive real number.\\ **Solution**\\ (i) False (ii) False (iii) True (iv) True (v) False (vi) Tr... and b are real numbers. (i) $(2+3i)+(7-2i)$ (ii) $2(5+4i)+3(7-4i)$ (iii) $-(-3+5i)-3(4+9i)$ (iv... -2i\\ &= 2+7+3i-2i\\ &= 9+i \end{array}$$ (ii) $$\begin{array}{cl} 2(5+4i)-3(7+4i) &= 10+8i
Exercise 2.1 (Solutions): 11 Hits, Last modified: 3 months ago; rational and irrational numbers: (i) $\sqrt{3}$ (ii) $\frac{1}{6}$ (iii) $\pi$ (iv) $\frac{15}{2}$ (v... ion into decimal fraction. (i) $\frac{17}{25}$ (ii) $\frac{19}{4}$ (iii)$\frac{57}{8}$ (iv) $\fr... frac{25}{38}$ **Soluation**\\ * (i) o.68 * (ii) 4.75 * (iii) 7.125 * (iv) 11.3889 * (v) 0.... * (i) $\frac{2}{3}$ is an irrational number. * (ii) $\pi$ is an irrational number. * (iii) $\frac{
Exercise 2.2 (Solutions): 6 Hits, Last modified: 3 months ago; following, * (i) $a + b = b + a$ ... ..... * (ii) $(ab)c = a(bc)$ ... ... ... * (iii) $7 \times ... .. ...... ( Commutative w.r.t addition) * (ii) $(ab)c = a(bc)$ ... ... ... (Associative w.r... ... ... (i)\\ &= 3x - 3x + 3y ... ... ... (ii)\\ &= 0 + 3y ... ... ... (iii)\\ &=... property of multiplication over subtraction * (ii) Commutative property * (iii) Additive inverse
Exercise 2.3 (Solutions): 6 Hits, Last modified: 3 months ago; (i) $\sqrt[3]{-64}$ *(ii) $2^{35}$\\ * (iii) $-7^\fra... 4} = -64^\frac{1}{3}$ ( Exponential form) * (ii) $2^\frac{3}{5} = \sqrt[5]{2}^{3}$ (Ra... * (i) $ 5^\frac{1}{5} = \sqrt{5}$\\ * (ii) $2^\frac{2}{3} = \sqrt[3]{4}$\\ * (iii) $\sqrt{... 7} = x^3$\\ **Solution**\\ * (i) False * (ii) True * (iii) False * (iv) False ====Ques
Exercise 2.5 (Solutions): 6 Hits, Last modified: 3 months ago; (i) $i^7$ (ii) $i^{50}$ (iii) $i^{12}$ ... &= {-1}^3 \cdot i\\ &= -i \end{array}$$ (ii) $$\begin{array}{cl} i^{50} &= (i^2 )^{25}\\ ... gate of the following numbers (i) $2 + 3i$ (ii) $3 - 5i$ (iii) $-i$ (iv) $-3 + 4i$ (v... cl} z = 2 + 3i\\ \bar{z} = 2 - 3i \end{array}$$ (ii) $$\begin{array}{cl} z = 3 - 5i\\ \bar{z} = 2 - 3
Exercise 2.4 (Solutions): 4 Hits, Last modified: 3 months ago; }(32)^{\frac{-1}{5}}}{\sqrt(196)^{-1}}$ * (ii) $\left(2x^5y^{-4}\right)\left(-8x^{-3}y^2\right)... ac{7}{27.\sqrt[3]{3}} \end{array}\end{array}$$ (ii) $$\begin{array}{cl} \left(2x^5y^{-4}\right)\lef... 0\right)^{1/2}\left(4\right)^{-1/3} 9^{1/4}}$ *(ii) $\sqrt\frac{{216}^{\frac{2}{3}}{25}^{\frac{1}{2}... 1+2/3}\\ &= 2^{3/3}\\ &= 2 \end{array}$$ (ii) $$\begin{array}{cl} \sqrt\frac{{216}^{2/3}{25}^{