Question Number 148951 by EDWIN88 last updated on 01/Aug/21

Let complex number z=(a+cos θ)+(2a−sin θ)i . If ∣z∣ ≤2 for any θ∈R then the range of real number a is ___

Answered by iloveisrael last updated on 01/Aug/21

Answered by mr W last updated on 01/Aug/21

(a+cos θ)^2 +(2a−sin θ)^2 ≤2^2 =4 5a^2 +2a(cos θ−2sin θ)−3≤0 5a^2 +2ka−3≤0 k=cos θ−2 sin θ=(√5)cos (θ+tan^(−1) 2) −(√5)≤k≤(√5) 5a^2 +2(√5)a−3≤0 ⇒a≤((√5)/5) 5a^2 −2(√5)a−3≤0 ⇒a≥−((√5)/5) ⇒−((√5)/5)≤a≤((√5)/5)

Commented bypuissant last updated on 01/Aug/21

nice prof..