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Question

Z2Z=1 then find the maximum and minimum value of |z|

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Solution

z2z=1
|z|2zz2z|z|+2z
Let |z|=r
r2r1r+2r
r+2r1
rϵR (i)
and r2r1
1r2r1
rϵ[1,2] (ii)
from (i) and (ii) rϵ[1,2]
rϵ[1,2]
|z|max=2,|z|min=1

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