The minimum value of mod z where mod z-2-2i =1?

mod(Z-2-2i) = 1                                .........1

let  2+2i =Z₁

  modZ₁ = sqrt8

then

 mod(Z-Z₁)=1

mod(Z-Z₁)<=modZ - modZ_{1                           (using formula)}

          1<=modZ - sqrt8

modZ >=1+sqrt8

its minimum value = (1+sqrt8)

Dear student,

mod z=3+2i

Hence its minimum value=root 13

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