Let |(( z )1-2( z )2)//(2-z1( z )2)|=...

Let `|(( z )_1-2( z )_2)//(2-z_1( z )_2)|=1a n d|z_2|!=1,w h e r ez_1a n dz_2` are complex numbers. Show that `|z_1|=2.`

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`|(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)`

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