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- Exercise 2.6 (Solutions)
- i) &= 2+3i+7-2i\\ &= 2+7+3i-2i\\ &= 9+i \end{array}$$ (ii) $$\begin{array}{cl} 2(5+4i)-3(7+4i... +8i-21-12i\\ &= 10-21+8i-12i\\ &= -11-4i \end{array}$$ (iii) $$\begin{array}{cl} -(-3+5i)-(4+9... = 3-5i-4-9i\\ &= 3-4-5i-9i\\ &= -1-14i \end{array}$$ (iv) $$\begin{array}{cl} 2i^2+6i^3+3i^{... imes12}(i)\\ &= -2 -6i+3+6i+4i\\ &= 1+4i \end{array}$$ ====Question 3==== * Simplify and writ
- Exercise 2.5 (Solutions)
- (i^2)^3\cdot i\\ &= {-1}^3 \cdot i\\ &= -i \end{array}$$ (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) $$\begin{array}{cl} (-i)^8 &= (-i^2 )^4\\ &= {-1}^4\\ &= 1 \end{array}$$ (v) $$\begin{array}{cl} (-i)^5 &= (-i)^
- Exercise 2.4 (Solutions)
- ^3.\sqrt[3]{3}}\\ &= \frac{7}{27.\sqrt[3]{3}} \end{array}\end{array}$$ (ii) $$\begin{array}{cl} \left(2x^5y^{-4}\right)\left(-8x^{-3}y^2\right) &=... &= -16x^2y^{-2}\\ &= \frac{-16x^2}{y^2} \end{array}$$ (iii) $$\begin{array}{cl} \left(\frac{x... -18} z^{-12}}\\ &=\frac{x^{18} z^{12}}{y^6} \end{array}$$ (iv) $$\begin{array}{cl} \frac{\left(81
- Exercise 2.3 (Solutions)
- {-5^3}\\ & = {-5}^{3\times\frac{1}{3}}\\ &= {-5} \end{array}$$ (ii) $$\begin{array}{cl} \sqrt[4]{32}... {1}{4}\right)\times\sqrt[4]{2}\\ &= 2\sqrt[4]{2} \end{array}$$ (iii) $$\begin{array}{cl} \sqrt[5]{\f... }}\right)^\frac{1}{5}\\ &= \frac{\sqrt[5]{3}}{2} \end{array}$$ (iv) $$\beg... eft(\frac{-2}{3}\right)^{3\times\frac{1}{3}}\\ &= \frac{-2}{3} \end{array}$$
- Exercise 2.2 (Solutions)
- . ... ... (iii)\\ &= 3y ... ... ... (iv) \end{array} $$ **Solution**\\ * (i) Distributive pr