Complex NumbersHard

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

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

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

Create a free account to view solution

View Solution Free
Topic: Complex Numbers·Practice all Complex Numbers questions

More Complex Numbers Questions

If is purely imaginary, then θ is equal to-...If | z1 | = 1, | z2 | = 2, | z3 | = 3 and | 9z1 z2 + 4z1z3 + z2z3 | = 12 then the value of | z1 + z2 + z3 | is equal to ...If complex numbers 1, −1 and i are represented by points A, B and C respectively on a compex plane, then they are ...If 2 cosθ = x + and 2 cos φ = y + , then...If complex numbers 2i, 5 + i and 4 represent points A, B and C respectively, then centroid of ᐃABC is-...