Question

If Z is a point on the circle |Z –1|= 1, then $\frac{Z - 2}{Z}$equals

• A. i tan (arg Z)
• B. i cot (arg Z)
• C. i tan (arg (Z –1))
• D. i cot (arg (Z –1))

Answer 1

Answer: (A)

i tan (arg Z)

Answer 2

Sol. |Z –1| = 1 Ž Z – 1 = e^iq

Ž $\frac{Z - 2}{Z}$= $\frac{e^{i\theta} - 1}{e^{i\theta} + 1}$ = $\frac{\cos\theta - 1 + i\sin\theta}{\cos\theta + 1 + i\sin\theta}$

= = i tan$\frac{\theta}{2}$

= i tan (arg Z)

(Q arg Z = arg (1 + cos q + i sin q) = arg

=$\frac{\theta}{2}$)