Complex NumbersMedium

Question

Let $S = \{ z:3 \leq |2z - 3(1 + i)| \leq 7\}$ be a set of complex numbers. Then ${Min}_{z \in S}\left| \left( z + \frac{1}{2}(5 + 3i) \right) \right|$ is equal to :

Options

A.$\frac{1}{2}$
B.$\frac{3}{2}$
C.2
D.$\frac{5}{2}$

Solution

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

$${{Min}_{z \in s}\left| z - \left( \frac{- 5}{2} - \frac{3}{2}i \right) \right| = PB }{PB = PC - \frac{7}{2} \Rightarrow 5 - \frac{7}{2} \Rightarrow \frac{3}{2} } $$

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