JEE Main 2024 Mathematics question

Mathematics Complex Numbers JEE Main 2024

Let z₁ and z₂ be two complex numbers such that z₁ + z₂ = 5 and z₁³ + z₂³ = 20 + 15i. Then |z₁⁴ + z₂⁴| equals

(A)75Correct
(B)25√3
(C)15√15
(D)30√3

Answer: (A)

Solution

z₁³ + z₂³ = (z₁ + z₂)³ − 3z₁z₂(z₁ + z₂) = 125 − 15z₁z₂ = 20 + 15i, so z₁z₂ = 7 − i. Then z₁² + z₂² = 25 − 2(7 − i) = 11 + 2i, and (z₁² + z₂²)²

See the full step-by-step solution

Create a free account to read the complete working, and practise questions like this in a timed test.

Create a free account

Question ID VK-017270