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Complex Numbers and Quadratic Equations · Question 57

JEE Main 2025 (Online) 29th January Morning ShiftMCQEasy📈 Topic in 45% papers+4−1
1

Let |z1 - 8 - 2i| 1 and |z2 - 2 + 6i| 2, z1, z2 C. Then the minimum value of |z1 - z2| is :

  1. 3
  2. 10
  3. 7
  4. 13

Answer

(3) 7

Solution

z1 lies in the disc with centre C1(8, 2), radius r1 = 1.

z2 lies in the disc with centre C2(2, -6), radius r2 = 2.

C1C2 = (8 - 2)2 + (2 + 6)2 = 36 + 64 = 10

C1C2 > r1 + r2, the discs do not meet.

|z1 - z2| = C1C2 - r1 - r2 = 10 - 3 = 7

Answer: (3)

JEE Main 2025 (Online) 29th January Morning Shift

Keep practising — Complex Numbers and Quadratic Equations

2

The sum, of the squares of all the roots of the equation x2 + |2x - 3| - 4 = 0, is

  1. 6(2 - 2)
  2. 3(3 - 2)
  3. 3(2 - 2)
  4. 6(3 - 2)
JEE Main 2025 (Online) 28th January Morning Shift
3

Let O be the origin, the point A be z1 = 3 + 2 2i, the point B(z2) be such that 3|z2| = |z1| and (z2) = (z1) + 6. Then

  1. area of triangle ABO is 114
  2. area of triangle ABO is 11 3
  3. ABO is a scalene triangle
  4. ABO is an obtuse angled isosceles triangle
JEE Main 2025 (Online) 28th January Morning Shift
4

If + i and + i are the roots of x2 - (3 - 2i)x - (2i - 2) = 0, i = -1, then + is equal to:

  1. 2
  2. -6
  3. 6
  4. -2
JEE Main 2025 (Online) 28th January Evening Shift

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