Let S = { z : 3 | 2 z - 3 ( 1 + i ) | 7 } be a set of complex numbers. Then min z S | ( z + 1 2 ( 5 + 3 i ) ) | is equal to: [2026]

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Solution

Q.
Let $S = {z : 3 \leq | 2 z - 3 (1 + i) | \leq 7}$ be a set of complex numbers. Then $\min_{z \in S}$ $| (z + \frac{1}{2} (5 + 3 i)) |$ is equal to: [2026]

1 $\frac{5}{2}$

2 $\frac{1}{2}$

3 $\frac{3}{2}$

4 $2$

Ans.
(3)

$\frac{3}{2} \leq$ $| z - \frac{3}{2} (1 + i) |$ $\leq \frac{7}{2}$

$\min_{z \in S}$ $| z - (\frac{- 5}{2} - \frac{3}{2} i) |$ $= P B$

$P B = P C - \frac{7}{2} \Rightarrow 5 - \frac{7}{2} = \frac{3}{2}$

$Option (3)$

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