If z ≠ 0 be a complex number such that z - 1 z = 2 , then the maximum value of z is

Step-by-step solution

Given z - 1 z = 2 We know that z - 1 z ≤ z - 1 z ≤ z + 1 z Let z = r i.e. r - 1 r ≤ 2 and r + 1 r ≥ 2 which is always true. Now r - 1 r ≤ 2 ⇒ r - 1 r ≥ - 2   &   r - 1 r ≤ 2 ⇒ r 2 - 1 ≤ 2 r ⇒ r - 1 2 ≤ 2 ⇒ r - 1 ≤ 2 ∴   z max = 1 + 2