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- Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
- exists}\; -z\in \mathbb{C} \mbox{ such that}\; z+\left( -z\right) =0 \\ \mbox{In fact if } z=a+bi, \mbox... ray}\nonumber\] - Associative Law for Addition \[\left( z+w\right) +v= z +\left( w+v\right)\nonumber \] </panel> <panel> **Question 2** Verify the multiplic... olutions** $\quad (2,6)\div (3,7)=\dfrac{(2,6)}{\left( 3,7 \right)}$ $=\dfrac{2+6i}{3+7i}=\dfrac{2+6i}
- Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
- \hline \end{array} \] **Solution** Suppose $G=\left\{ 0,1,2,3 \right\}$ i) The given table show that... n \mathbb{Z}$, $a+b\in \mathbb{Z}$. b- Since $a+\left( b+c \right)=\left( a+b \right)+c$, thus associative law holds in $\mathbb{Z}$. c- Since $0\in \mathb... ble represents the sums of the elements of set $\left\{ E,O \right\}$. The identity element of the set
- Exercise 1.1 (Solutions) @fsc-part1-ptb:sol:ch01
- imes$'. ---- (ix) $a(b-c)= ab-ac$ **Property:** Left distributive property. ---- (x) $(x-y)z= xz-yz$ ... . ---- (xii) $a(b+c-d)= ab+ac-ad$ **Property:** Left distributive property. </panel> <panel> **Quest... + 1 \times \frac{c}{d}\\ &= \frac{a}{b} \times \left(d \times \frac{1}{d}\right)+\left(b \times \frac{1}{b}\right)\times \frac{c}{d}\\ &= \frac{a}{b} \time