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- Exercise 2.1 (Solutions)
- h of the following are rational and irrational numbers: (i) $\sqrt{3}$ (ii) $\frac{1}{6}$ (iii) $\pi$... alse? * (i) $\frac{2}{3}$ is an irrational number. * (ii) $\pi$ is an irrational number. * (iii) $\frac{1}{9}$ is a terminating fraction. * (iv)... on**\\ * (i) $\frac{2}{3}$ is an irrational number. **False** * (ii) $\pi$ is an irrational numbe
- Exercise 2.6 (Solutions)
- i^2) is (-1 + 6i)$\\ (v) Difference of complex numbers $z = a + ib$ and its conjugate is a real number.\\ (vi) If $(a-1)-(b+3)i = 5+8i$, then a = 6 & b = -11\\ (vii) Product of complex number and its conjugate is always a non-negative real number.\\ **Solution**\\ (i) False (ii) False (iii
- Exercise 2.5 (Solutions)
- (vi) $i^{27}$ **Solution**\\ (i) $$\begin{array}{cl} i^7 &= {i^6}\cdot i\\ &= (i^2)^3... {-1}^3 \cdot i\\ &= -i \end{array}$$ (ii) $$\begin{array}{cl} i^{50} &= (i^2 )^{25}\\ &= {-1}^{25}\\ &= -1 \end{array}$$ (iii) $$\begin{array}{cl} i^{12} &= (i^2 )^6\\ &= {-1}^6\\ &= 1 \end{array}$$ (iv) $$\begin{array}{cl} (-i)^8 &= (-i^2 )^4\\ &= {-1
- Exercise 2.4 (Solutions)
- right)\left(3^3\right)}$ **Solution**\\ (i) $$\begin{array}{cl} \begin{array}{cl} \frac{(243)^{\frac{-2}{3}}(32)^{\frac{-1}{5}}}{\sqrt(196)^{-1}} &=... .\sqrt[3]{3}} \end{array}\end{array}$$ (ii) $$\begin{array}{cl} \left(2x^5y^{-4}\right)\left(-8x^{-... &= \frac{-16x^2}{y^2} \end{array}$$ (iii) $$\begin{array}{cl} \left(\frac{x^{-2}y^{-1}z^{-4}}{x^4
- Exercise 2.3 (Solutions)
- rt[3]{\frac{-8}{27}}$ **Soluton**\\ (i) $$\begin{array}{cl} \sqrt[3]{-125} &= \sqrt[3]{-5^3}\\ ... es\frac{1}{3}}\\ &= {-5} \end{array}$$ (ii) $$\begin{array}{cl} \sqrt[4]{32} &= \sqrt[4]{{2}^5}\\ &... 4]{2}\\ &= 2\sqrt[4]{2} \end{array}$$ (iii) $$\begin{array}{cl} \sqrt[5]{\frac{3}{32}} &= \left(\fr... end{array}$$ (iv) $$\begin{array}{cl} \sqrt[3]{\frac{-8}{27}} &= \sqrt[3]
- Exercise 2.2 (Solutions)
- g blanks by stating the properties of the real numbers used, $$ \begin{array}{cl} 3x + 3(y - x) &= 3x + 3y - 3x ... ... ... (i)\\ &= 3x - 3x + 3y ... .. * (iv) $\sqrt{3} \times \sqrt{3}$ is real number ... .... .... * (v) $\left(\frac{-5}{8} \right