Let `|(z_(1) - 2z_(2))//(2-z_(1)z_(2))|= 1` and `|z_(2)| ne 1`, where `z_(1)` and `z_(2)` are complex numbers. shown that `|z_(1)| = 2`

Explanation

`|(bar(z)_(1)-2bar(z)_(2))/(2-z_(1)bar(z)_(2))|=1`
or `|bar(z)_(1)-2bar(z)_(2)|^(2)=|2-z_(1)bar(z)_(2)|^(2)`
or `(bar(z)_(1)-2bar(z)_(2))(bar(bar(z)_(1)-2bar(z)_(2)))=(2-z_(1)bar(z)_(2))(bar(2-z_(1)bar(z)_(2)))`
or `(bar(z)_(1)-2bar(z)_(2))(z_(1)-2z_(2))=(2-z_(1)bar(z)_(2))(2-bar(z)_(1)z_(2))`
or ` z_(1)bar(z)_(1)-2bar(z)_(1)z_(2)-2z_(1)bar(z)_(2)+4z_(2)bar(z)_(2)=4-2bar(z)_(1)z_(2)-2z_(1)bar(z)_(2)+z_(1)bar(z)_(1)z_(2)bar(z)_(2)`
or `|z_(1)|^(2)+4|z_(2)|^(2)=4+|z_(1)|^(2)|z_(2)|^(2)`
or `|z_(1)|^(2)-|z_(1)|^(2)|z_(2)|^(2)+4|z_(2)|^(2)-4=0`
or `|z_(1)|^(2)"("1-|z_(2)|^(2)")"+4(|z_(2)|-1)=0`
or `"("|z_(2)|^(2)-1")""("|z_(1)|^(2)-4")"=0`
or `|z_(1)|=2" "("as "|z_(2)|ne1)`