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 z = , then -...If z1 = , a ≠ 0 and z2 = , b ≠ 0 are such that z1 = then -...If z is a complex number then the equation z2 + z |z| + |z2| = 0 is satisfied by(ω and ω2 are imaginary cube r...Let z be the complex number satisfying $|z - 5| \leq 3$ and having maximum positive principal argument.Then $34\left| \f...The system of equations , where z is a complex number has :...