I=sqrt((1-i)/(1+i sqrt(3)))quad z_(2)=sqrt((1-i)/(sqrt(3)+i))quad Z_(3)=sqrt((1+i)/(sqrt(3)-i))

For Z_(1)=6sqrt((1-i)/(1+i sqrt(3)));Z_(2)=6sqrt((1-i)/(sqrt(3)+i));Z_(3)=6sqrt((1+i)/(sqrt(3)-i)) which of the following holds good?

For z_(1)=""^(6)sqrt((1-i)//(1+isqrt(3))),z_(2)=""^(6)sqrt((1-i)//(sqrt(3)+i)) , z_(3)= ""^(6)sqrt((1+i) //(sqrt(3)-i)) , prove that |z_(1)|=|z_(2)|=|z_(3)|

For z_(1)=""^(6)sqrt((1-i)//(1+isqrt(3))),z_(2)=""^(6)sqrt((1-i)//(sqrt(3)+i)) , z_(3)= ""^(6)sqrt((1+i) //(sqrt(3)-i)) , prove that |z_(1)|=|z_(2)|=|z_(3)|

(sqrt(3)+i)/((1+i)(1+sqrt(3)i))|=

Let z_(1)=(2sqrt(3)+ i6sqrt(7))/(6sqrt(7)+ i2sqrt(3))" and "z_(2)=(sqrt(11)+ i3sqrt(13))/(3sqrt(13)- isqrt(11)) . Then |(1)/(z_1)+(1)/(z_2)| is equal to

((sqrt(3)+i sqrt(5))(sqrt(3)-i sqrt(5)))/((sqrt(3)+sqrt(2)i)-(sqrt(3)-i sqrt(2))

( (sqrt(2)+i sqrt(3))+(sqrt(2)-i sqrt(3)) )/( (sqrt(3)+i sqrt(2))+(sqrt(3)-i sqrt(2)) )

log((1+i sqrt(3))/(1-i sqrt(3)))

((3+i sqrt(3))(3-i sqrt(3)))/((sqrt(3)+sqrt(2)i)-(sqrt(3)-i sqrt(2)))