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Exercise 2.6 (Solutions): 27 Hits, Last modified: 17 months ago; +3i^{16}-6i^{19}+4i^{25}$ **Solution**\\ (i) $$\begin{array}{cl} (2+3i)+(7-2i) &= 2+3i+7-2i\\ &= 2+7+3i-2i\\ &= 9+i \end{array}$$ (ii) $$\begin{array}{cl} 2(5+4i)-3(7+4i) &= 10+8i-21-12i... 21+8i-12i\\ &= -11-4i \end{array}$$ (iii) $$\begin{array}{cl} -(-3+5i)-(4+9i) &= 3-5i-4-9i\\... 3-4-5i-9i\\ &= -1-14i \end{array}$$ (iv) $$\begin{array}{cl} 2i^2+6i^3+3i^{16}-6i^{19}+4i^{25}
Exercise 2.5 (Solutions): 18 Hits, Last modified: 17 months ago; (vi) $i^{27}$ **Solution**\\ (i) $$\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 2.1 (Solutions): 14 Hits, Last modified: 17 months ago; ational number $\frac{2}{3}$ , divide unit length between 0 and 1 into 3 equal parts. - (ii) Take 2 ... tional number $-\frac{4}{5}$ , divide unit length between 0 and -1 into 5 equal parts. - Take 4 part... (iii) - Rational number $\frac{3}{4}$ lies between 1 and 2 on the number line. - The distance between 1 and 2 is divided into 4 equal parts , from
Exercise 2.4 (Solutions): 10 Hits, Last modified: 17 months ago; 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) $$\begin{array}{cl} \left(\frac{x^{-2}y^{-1}z^{-4}}{x^4
Exercise 2.3 (Solutions): 4 Hits, Last modified: 17 months ago; rt[3]{\frac{-8}{27}}$ **Soluton**\\ (i) $$\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): 1 Hits, Last modified: 17 months ago; ting the properties of the real numbers used, $$ \begin{array}{cl} 3x + 3(y - x) &= 3x + 3y - 3x ...