Question

If |z –1| £ 2 and |wz –1 – w²| = a (wherew is cube root of unity) then

• A. $\frac{1}{2}$£ a £ 3
• B. 0 £ a £ 4
• C. 0 £ a £$\frac{1}{2}$+ $\frac{\sqrt{3}}{2}$
• D. None of these

Answer 1

Answer: (B)

0 £ a £ 4

Answer 2

Sol.\ |wz –1 –w²| = a Ž |wz + w| = a Ž |z + 1| = a

Ž |z – 1 + 2| = a

|z –1| + 2 ³ a

Ž a £ 4 … (1)

Now |z + 1| ³ 0

\ a ³ 0 … (2)

from (1) and (2)

\ 0 £ a £ 4