The least value of z where z is complex number which satisfies the inequality e z + 3 z - 1 z + 1 log e 2 ≥ log 2 5 7 + 9 i , i = - 1 , is equal to :

Step-by-step solution

e z + 3 z - 1 z + 1 log e 2 ≥ log 2 5 7 + 9 i ⇒ 2 z + 3 z - 1 z + 1 ≥ l o g 2 16 ⇒ 2 z + 3 z - 1 z + 1 ≥ 2 3 z + 3 z - 1 z + 1 ≥ 3 z + 3 z - 1 ≥ 3 z + 1 z 2 + 2 z - 3 ≥ 3 z + 3 ⇒ z 2 + z - 6 ≥ 0 ⇒ z - 3 z + 2 ≥ 0 ⇒ z - 3 ≥ 0 ⇒ z ≥ 3    ⇒ z min = 3