Match the items in Column A with Column B using the table below.
| Column A | Column B |
|---|---|
(a) The polar form of \(i + \sqrt{3}\) | (i) Perpendicular bisector of segment joining \((-2,0)\) and \((2,0)\) |
(b) The amplitude of \(-1 + \sqrt{3}\) is | (ii) On or outside the circle having centre at \((0,-4)\) and radius 3 |
(c) If \(|z + 2| = |z - 2|\), then locus of \(z\) is | (iii) \(\dfrac{2\pi}{3}\) |
(d) If \(|z + 2i| = |z - 2i|\), then locus of \(z\) is | (iv) Perpendicular bisector of segment joining \((0,-2)\) and \((0,2)\) |
(e) Region represented by \(|z + 4i| \ge 3\) is | (v) \(2\bigl(\cos\tfrac{\pi}{6} + i\sin\tfrac{\pi}{6}\bigr)\) |
(f) Region represented by \(|z + 4| \le 3\) is | (vi) On or inside the circle having centre \((-4,0)\) and radius 3 units |
(g) Conjugate of \(\dfrac{1 + 2i}{1 - i}\) lies in | (vii) First quadrant |
(h) Reciprocal of \(1 - i\) lies in | (viii) Third quadrant |
| Column A | Matched Item from Column B |
|---|---|
(a) The polar form of \(i + \sqrt{3}\) | (v) \(2\bigl(\cos\tfrac{\pi}{6} + i\sin\tfrac{\pi}{6}\bigr)\) |
(b) The amplitude of \(-1 + \sqrt{3}\) is | (iii) \(\dfrac{2\pi}{3}\) |
(c) If \(|z + 2| = |z - 2|\), then locus of \(z\) is | (i) Perpendicular bisector of segment joining \((-2,0)\) and \((2,0)\) |
(d) If \(|z + 2i| = |z - 2i|\), then locus of \(z\) is | (iv) Perpendicular bisector of segment joining \((0,-2)\) and \((0,2)\) |
(e) Region represented by \(|z + 4i| \ge 3\) is | (ii) On or outside the circle having centre at \((0,-4)\) and radius 3 |
(f) Region represented by \(|z + 4| \le 3\) is | (vi) On or inside the circle having centre \((-4,0)\) and radius 3 units |
(g) Conjugate of \(\dfrac{1 + 2i}{1 - i}\) lies in | (viii) Third quadrant |
(h) Reciprocal of \(1 - i\) lies in | (vii) First quadrant |