Question

If | z – 2 | = min {| z – 1|, | z – 5 |}, where z is a complex number, then-

• A. Re (z) = $\frac{3}{2}$
• B. Re (z) = $\frac{7}{2}$
• C. Re (z) Ī$\left\{ \frac{3}{2},\frac{7}{2} \right\}$
• D. None of these

Answer 1

Answer: (C)

Re (z) Ī$\left\{ \frac{3}{2},\frac{7}{2} \right\}$

Answer 2

Sol. | z – 2 | = min {| z – 1 |, | z – 5 |}

i.e., | z – 2| = | z – 1|, where | z – 1| < | z – 5|

Ž Re(z) = $\frac{3}{2}$ which satisfy | z – 1| < |z – 5 |.

Also, | z – 2| = | z – 5 |, where| z – 5 | < | z – 1|.

Ž Re(z) = $\frac{7}{2}$ which satisfy | z – 5 | < | z – 1 |.