The least value of z where z is complex number which satisfies the inequality e z + 3 z - 1 z + 1 log e 2…

The least value of z where z is complex number which satisfies the inequality ez+3z-1z+1loge2≥log257+9i, i=-1, is equal to :

  1. 3
  2. 5
  3. 2
  4. 8

Solution

ez+3z-1z+1loge2≥log257+9i

⇒2z+3z-1z+1≥log216

⇒2z+3z-1z+1≥23

z+3z-1z+1≥3

z+3z-1≥3z+1

z2+2z-3≥3z+3

⇒z2+z-6≥0

⇒z-3z+2≥0⇒z-3≥0

⇒z≥3  ⇒zmin=3

Asked in: JEE Main 2021 (16 Mar Shift 2)

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