log21((∣z∣−1)2∣z∣+11)≤2
⇒(∣z∣−1)2∣z∣+11≥21, ∵loga(b)≤c⇒b≥acif0<a<1
⇒2∣z∣+22≥(∣z∣−1)2, {\because |z|\neq 1&{(|z|-1)}^{2}>0}
⇒2∣z∣+22≥∣z∣2+1−2∣z∣
⇒∣z∣2−4∣z∣−21≤0
⇒(∣z∣−7)(∣z∣+3)≤0
⇒∣z∣≤7
∴ Largest value of ∣z∣ is 7
Let a complex number z,∣z∣=1, satisfy log21((∣z∣−1)2∣z∣+11)≤2. Then, the largest value of ∣z∣ is equal to _________.
Held on 16 Mar 2021 · Verified 6 Jul 2026.
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