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(i) w=\dfrac{z+i}{z-i} \Rightarrow z=\left( \dfrac{w+1}{w-1} \right)i \text{ and }|z-i|=2 \Rightarrow \left|\dfrac{w+1}{w-1}i-i\right|=2 \Rightarrow left| \dfrac{2i}{w-1} \right|=2
[br]f'(x) = 2ax + b \\[br]f(1) = a + b + c \\[br]f(-1) = a - b + c \\[br]f(0) = c[br]
(1+e)u_1cos\theta=2v_2[br]\Rightarrow (1+e)cot\theta sin\phi v_1=2(eu_1cos\theta+v_1cos\phi)[br]\Rightarrow (1+e)cot\theta sin\phi =2ecot\thetasin\phi+2cos\phi[br]\Rightarrow (1-e)cot\theta=2cot\phi[br]\Rightarrow tan\theta=\frac{1-e}{2}tan\phi
tank=\frac{tan\phi-tan\theta}{1+tan\phitan\theta}=tan\theta \frac{(1+e)/(1-e)}{1+(2/(1-e))Tan^2\theta}
\mathbf{w}&\mathbf{g}
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