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Exercise 1.1 (Solutions)

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rac{b}{c} = \frac{a+b}{c}$$. **Solution** \begin{align} L.H.S &= \frac{a}{c}+\frac{b}{c}\\ &= a \times... ibutive property)}\\ &= \frac{a+b}{c}=R.H.S \end{align} **Question 4(ii)** Prove the following rules o... ac{c}{d}=\frac{ad+bc}{bd}$$. **Solution** \begin{align} L.H.S &= \frac{a}{b}+\frac{c}{d}\\ &= \frac{a}... s \frac{1}{bd} \\ &= \frac{ad+bc}{bd}=R.H.S \end{align} </panel> <panel> **Question 5** Prove that $

Exercise 1.2 (Solutions)

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)** Simplify: ${-i}^{19}$ **Solutions** \begin{align} {-i}^{19}& =[(-1)(i)] ^{19}=(-1)^{19}\cdot i^{1... 2)^{9} \cdot i \\ & =-(-1)^{9} i=-(-1)i =i. \end{align} **Question 4(iv)** Simplify: $\displaystyle {{(-1)}^{-\frac{21}{2}}}$ **Solution** \begin{align} (-1)^{-\frac{21}{2}}&=\frac{1}{(-1)^\frac{21}{2... ac{i}{i}\\ &=\frac{i}{i^2}=\frac{i}{-1}=-i. \end{align} </panel> <panel> **Question 5(i)** Write $\sq