JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(z\) be a complex number such that \(|z+2| = |z-2|\) and \(\arg\left(\dfrac{z+3}{z-i}\right) = \dfrac{\pi}{4}\). Then \(|z|^2\) is equal to:
- A \(9\)
- B \(4\)
- C \(5\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(9\)
Step-by-step Solution
Detailed explanation
Given \(|z+2| = |z-2|\), the point \(z\) lies on the perpendicular bisector of the line segment joining \((-2, 0)\) and \((2, 0)\). This means \(z\) lies on the imaginary axis. Let \(z = iy\), where \(y \in \mathbb{R}\). We are given…
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