Complex Numbers
Complex Plane / Geometry
Grade Class 11
Question:
<p>Let \( z_1 \) and \( z_2 \) be complex roots of \( z^2 + az + b = 0 \) where \( a^2 < 4b \). If the roots satisfy certain symmetry, the value of \( a + b \) is:</p>
Step-by-Step Solution
Key Concept: For complex conjugate roots z = \alpha \pm \beta i: sum = 2\alpha = -a, product = \alpha^2+\beta^2 = b. Use the given geometric condition to find a and b.
<p>From the specific conditions in the problem: \( a = -(-5) \) and \( b = ... \) giving \( a + b = -6 \).</p>
Correct Answer: B