Let z C be such that |z|<1. If = 5+3z5(1-z), then:

Correct answer: C. (c) JEE Main 2019 = 5+3z5-3z ⇒5 -5 ωz=5+3z ⇒5 -5=z(3+5 ) ⇒z= 5( -1)3+5 ∵ (z ) 25 ⇒2 Re ( )> 25 ⇒ Re ( )> 15

JEE Previous Year Question

$Let z \in C be such that ∣ z ∣ < 1 . If ω = \frac{5 + 3 z}{5 ( 1 - z )}, then:$

Topic: JEE PYQ

Answer: C. Full step-by-step solution below.

Correct answer: C

(c) JEE Main 2019 ω = \frac{5 + 3 z}{5 - 3 z} \Rightarrow 5 ω - 5 ωz = 5 + 3 z \Rightarrow 5 ω - 5 = z (3 + 5 ω) \Rightarrow z = \frac{5 ( ω - 1 )}{3 + 5 ω} ∵ (z) < 1, ∴ 5 (ω - 1) < (3 + 5 ω) \Rightarrow 25 (ω ω - ω - ω + 1) < 9 + 25 ω ω + 15 ω + 15 ω (∵ (z)^{2} = z z) \Rightarrow 16 < 40 ω + 40 ω \Rightarrow ω + ω > \frac{2}{5} \Rightarrow 2 Re (ω) > \frac{2}{5} \Rightarrow Re (ω) > \frac{1}{5}