JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(z_1, z_2 \in \mathbb{C}\) be the distinct solutions of the equation \(z^2 + 4z - (1 + 12i) = 0\). Then \(|z_1|^2 + |z_2|^2\) is equal to :
- A \(18\)
- B \(22\)
- C \(29\)
- D \(34\)
Answer & Solution
Correct Answer
(D) \(34\)
Step-by-step Solution
Detailed explanation
Given equation is \(z^2 + 4z - (1 + 12i) = 0\) Let the roots be \(z_1\) and \(z_2\). Sum of roots: \(z_1 + z_2 = -4\) Product of roots: \(z_1 z_2 = -(1 + 12i)\) We know that \((z_1 - z_2)^2 = (z_1 + z_2)^2 - 4z_1 z_2\)…
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