Exams › JEE Main › Maths

For a complex number z = x + iy with x, y real, find the minimum value of the expression E = |z|² + |z - 3|² + |z - 6i|².

1. 30
2. 24
3. 36
4. 45

Correct answer: 30

Solution

E is the sum of squared distances from (x,y) to (0,0), (3,0), (0,6); this is minimized at the centroid (1,2), giving E = 30.

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 →