∣∣∣Z−2Z∣∣∣=1 then find the maximum and minimum value of |z|
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Solution
∣∣∣z−2z∣∣∣=1 ∣∣∣|z|−∣∣∣2z∣∣∣∣∣∣≤∣∣∣z−2z∣∣∣≤|z|+∣∣∣−2z∣∣∣ Let |z|=r ⇒∣∣∣r−2r∣∣∣≤1≤r+2r r+2r≥1 ⇒rϵR (i) and ∣∣∣r−2r∣∣∣≤1 ⇒−1≤r−2r≤1 ⇒rϵ[1,2] (ii) ∴ from (i) and (ii) rϵ[1,2] rϵ[1,2] |z|max=2,|z|min=1