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Question #40494

Difficulty: 8/10 | 🟢 Free

The Question

Let $z_1$ and $z_2$ be the roots of the complex quadratic equation $z^2 - (1+3i)z - 2 + 2i = 0$ . The value of $|z_1| + |z_2|$ is:

Options

A.
$2 + \sqrt{2}$
B.
2^{7/4}
C.
$\sqrt{10}$
D.
6

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Specialist

Targeted practice for niche, high-difficulty concepts that frequently appear in JEE Advanced exams.

Concepts Behind This Question

Conjugate Root Theorem|Quadratic Equations with Complex Coefficients|Modulus Function Symmetry

Why This Question Is Tricky

Common Mistakes

This question tests the boundary conditions of the Conjugate Root Theorem.

A common reflex among students is to assume that the roots of any quadratic equation are complex conjugates, which implies $|z_1| = |z_2|$ .

If applied here, students would use the product of roots $|z_1 z_2| = |-2+2i| = 2\sqrt{2}$ , deduce $|z_1| = 2^{3/4}$ , and incorrectly conclude the sum is $2^{7/4}$ .

The trap penalizes rote memorization by using complex coefficients, breaking the symmetry and forcing a rigorous application of the quadratic formula and modulus definition.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Complex Numbers and Quadratic Equations - Class 11
Concept	Conjugate Root Theorem
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free