The least value of z, where ‘z’ is complex number which satisfies the in-equality         expz+3z−1z+1loge2≥log257+9i,  i=−1,   is equal to:

The given inequality is expz+3z−1z+1loge2≥log257+9i,  i=−1,⇒2z+3z-1z+1≥log2175+81     ⇒2z+3z−1z+1≥23       ⇒z+3z−1z+1≥3             ⇒z2+2z−3≥3z+3⇒z2−z−6≥0     ⇒z−3z+2≥0 ⇒z-3≥0 ⇒z≥3