Question:medium
Let \( S = \{z : 3 \le |2z - 3(1+i)| \le 7\ \) be a set of complex numbers. Then \( \min_{z \in S} \left| z + \frac{1}{2}(5+3i) \right| \) is equal to :}
Let \( S = \{z : 3 \le |2z - 3(1+i)| \le 7\ \) be a set of complex numbers. Then \( \min_{z \in S} \left| z + \frac{1}{2}(5+3i) \right| \) is equal to :}
Show Hint
Always plot the center and the given point on a rough Argand plane. It helps you instantly see if you need to subtract the radius from the distance or vice versa.
Updated On: Apr 1, 2026
- 2
- \( \frac{3}{2} \)
- \( \frac{1}{2} \)
- \( \frac{5}{2} \)
Show Solution
The Correct Option is A
Solution and Explanation
Was this answer helpful?
0
Top Questions on Coordinate Geometry
- Let \( y = x \) be the equation of a chord of the circle \( C_1 \) (in the closed half-plane \( x \ge 0 \)) of diameter 10 passing through the origin. Let \( C_2 \) be another circle described on the given chord as diameter. If the equation of the chord of the circle \( C_2 \), which passes through the point \( (2, 3) \) and is farthest from the center of \( C_2 \), is \( x + ay + b = 0 \), then \( b \) is equal to:
- JEE Main - 2026
- Mathematics
- Coordinate Geometry
- Number of solutions of \( \sqrt{3} \cos 2\theta + 8 \cos \theta + 3\sqrt{3} = 0, \theta \in [-3\pi, 2\pi] \) is:
- JEE Main - 2026
- Mathematics
- Coordinate Geometry
- The number of elements in the relation \[ R=\{(x,y): 4x^2+y^2<52,\; x,y\in\mathbb{Z}\} \] is
- JEE Main - 2026
- Mathematics
- Coordinate Geometry
- Given conic \(x^2 - y^2 \sec^2 \theta = 8\) whose eccentricity is '\(e_1\)' & length of latus rectum '\(l_1\)' and for conic \(x^2 + y^2 \sec^2 \theta = 6\), eccentricity is '\(e_2\)' & length of latus rectum '\(l_2\)'. If \(e_1^2 = e_2^2 (1 + \sec^2 \theta)\) then value of \(\frac{e_1 l_1}{e_2 l_2} \tan \theta\)
- JEE Main - 2026
- Mathematics
- Coordinate Geometry
- Want to practice more? Try solving extra ecology questions todayView All Questions
Questions Asked in JEE Main exam
In an equilateral prism the path of a ray is shown in the figure. Determine the refractive index of the prism.
- JEE Main - 2026
- Ray optics and optical instruments
