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- Exercise 2.6 (Solutions)
- e or false. (i) $\sqrt{-3}\cdot\sqrt{-3} = 3$\\ (ii) $i^{73}=-i$\\ (iii) $i^{10} = -1$\\ (iv) Complex conjugate of $(-6i + i^2) is (-1 + 6i)$\\ (v) Diff... f $(a-1)-(b+3)i = 5+8i$, then a = 6 & b = -11\\ (vii) Product of complex number and its conjugate is a... tive real number.\\ **Solution**\\ (i) False (ii) False (iii) True (iv) True (v) False (vi) Tr
- Exercise 2.1 (Solutions)
- rational and irrational numbers: (i) $\sqrt{3}$ (ii) $\frac{1}{6}$ (iii) $\pi$ (iv) $\frac{15}{2}$ (v) $7.25$ (vi)$\sqrt{29}$ **Solution**\\ * Ratio... ion into decimal fraction. (i) $\frac{17}{25}$ (ii) $\frac{19}{4}$ (iii)$\frac{57}{8}$ (iv) $\frac{205}{18}$ (v) $\frac{5}{8}$ (vi) $\frac{25}{38
- Exercise 2.2 (Solutions)
- following, * (i) $a + b = b + a$ ... ..... * (ii) $(ab)c = a(bc)$ ... ... ... * (iii) $7 \times 1 = 7$ ... ... ... * (iv) $x > y$ or $x = y$ or $x... + c = b + c \Rightarrow a = b$ ... ... ... * (vii) $5 + (-5) = 0$ ... ... ... * (viii) $7 \times \frac{1}{7} = 1$ ... ... ... * (ix) $a > b \Righta
- Exercise 2.3 (Solutions)
- (i) $\sqrt[3]{-64}$ *(ii) $2^{35}$\\ * (iii) $-7^\frac{1}{3}$ * (iv) $y^\frac{-... 4} = -64^\frac{1}{3}$ ( Exponential form) * (ii) $2^\frac{3}{5} = \sqrt[5]{2}^{3}$ (Radical form) * (iii) $-7^\frac{1}{3} = -\sqrt[3]{7}$ (Rad
- Exercise 2.5 (Solutions)
- (i) $i^7$ (ii) $i^{50}$ (iii) $i^{12}$ (iv) $... &= {-1}^3 \cdot i\\ &= -i \end{array}$$ (ii) $$\begin{array}{cl} i^{50} &= (i^2 )^{25}\\ &= {-1}^{25}\\ &= -1 \end{array}$$ (iii) $$\begin{array}{cl} i^{12} &= (i^2 )^6\\
- Exercise 2.4 (Solutions)
- }(32)^{\frac{-1}{5}}}{\sqrt(196)^{-1}}$ * (ii) $\left(2x^5y^{-4}\right)\left(-8x^{-3}y^2\right)$ * (iii) $\left(\frac{x^{-2}y^{-1}z^{-4}}{x^4y^{-3}z^0}\... ac{7}{27.\sqrt[3]{3}} \end{array}\end{array}$$ (ii) $$\begin{array}{cl} \left(2x^5y^{-4}\right)\lef... ^{-2}\\ &= \frac{-16x^2}{y^2} \end{array}$$ (iii) $$\begin{array}{cl} \left(\frac{x^{-2}y^{-1}z^{