Question13. Given that $Z_{1}=(3-2 i), Z_{2}=(-2+4 \mathrm{i})$ a. workout i. $Z_{1}+Z_{2}$ (2 marks) ii. $Z_{1}-Z_{2}$ (2 marks) $\qquad$ $\qquad$ $\qquad$ $\qquad$ b. Represent the following in triangle diagram i. $Z_{1}+Z_{2}$ (2 marks) $\qquad$ $\qquad$ $\qquad$ ii. $Z_{1}-Z_{2} \quad$ (2marks) $\qquad$ $\qquad$ Page 5 of 10 $\qquad$ $\qquad$ $\qquad$ $\qquad$ c. Put $\frac{2-i}{1-i}$ in the form $\mathrm{a}+\mathrm{ib}$ and hence find the values of $\mathbf{a}$ and $\mathbf{b}$. (4 marks) $\qquad$ $\qquad$ $\qquad$ $\qquad$
14. a. Differentiate from the first principles $y=4-x^{2}$ (3 marks) $\qquad$ $\qquad$ $\qquad$ $\qquad$ b. A point moving in a straight line such that the distance $S$ covered after $t$ seconds from the fixed point on the line is given by the equation $\mathrm{S}=\left(t^{3}-2 t^{2}+t\right)$ meters, find i. Velocity after three seconds. (3 marks) $\qquad$ $\qquad$ $\qquad$