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Exercise 1.1 (Solutions)

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or '$\times$'. **Solutions** Addition Table \[\begin{array}{|c|c|} \hline + & 0 \\ \hline 0 & 0 \\ ... ure property w.r.t. '+'. Multiplication Table \[\begin{array}{|c|c|} \hline \times & 0 \\ \hline 0 & ... or '$\times$'. **Solutions** Addition Table \[\begin{array}{|c|c|} \hline + & 1 \\ \hline 1 & 2 \\ ... ure property w.r.t. '+'. Multiplication Table \[\begin{array}{|c|c|} \hline \times & 1 \\ \hline 1 &

Exercise 1.2 (Solutions)

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=z\nonumber \] - Existence of Additive Inverse \[\begin{array}{l} \mbox{For each} \; z\in \mathbb{C}, \mb... 4(iii)** Simplify: ${-i}^{19}$ **Solutions** \begin{align} {-i}^{19}& =[(-1)(i)] ^{19}=(-1)^{19}\cdo... laystyle {{(-1)}^{-\frac{21}{2}}}$ **Solution** \begin{align} (-1)^{-\frac{21}{2}}&=\frac{1}{(-1)^\frac... \overline{z }=x-iy$, where $x,y\in \mathbb{R}$ \begin{align} \text{Sum} &=z+\overline{z}\\ &=x+iy+x-i