Exams › JEE Main › Maths

(a) Let z = x + iy with x, y real. Define A = { z: |z| <= 2 } and B = { z: (1 - i)z + (1 + i)conj(z) >= 4 }. Find the area of A intersect B. (b) For a non-real complex number z, find the minimum value of Im(z⁵)/Im(z).

1. (a) 2pi - 2; (b) -1
2. (a) pi - 2; (b) -4
3. (a) 2pi - 4; (b) -5
4. (a) 4pi - 2; (b) -2

Correct answer: (a) pi - 2; (b) -4

Solution

Region B is the half-plane x + y >= 2; intersected with the disk of radius 2 it is a circular segment of area pi - 2. For part (b) the minimum of Im(z⁵)/Im(z) is -4.

Related JEE Main Maths questions

• Given z1 = √3 + i√3 and z2 = √3 + i, determine the quadrant in which the complex number z1/z2 lies.
• For the quadratic equation 2(1+i)x² − 4(2−i)x − (5+3i) = 0, the root with the larger absolute value is
• Find the value of ((cosθ+isinθ)⁴)/((cosθ-isinθ)³).
• How many complex numbers z satisfy the equation z³ + (3|z|²)/(z) = 0, given that |z| = √(3)?
• Let z = x + iy be a variable complex number. If arg((z - 1)/(z + 1)) = π/4, then which relation is satisfied?
• For positive values of a, b and c, consider the quadratic equation ax² + bx + c = 0. What can be said about its two roots?

⚔️ Practice JEE Main Maths free + battle 1v1 →