[" For "z_(1)=root(6)((1-i)/(1+i sqrt(3))),z_(2)=root(6)((1-i)/(sqrt(3)+i))],[z_(3)=root(6)((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)|

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)=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?

If z_(1)=sqrt(3)-i, z_(2)=1+i sqrt(3) , then amp (z_(1)+z_(2))=

If |z-3i|

If z_(1)=iz_(2) and z_(1)-z_(3)=i(z_(3)-z_(2)), then prove that |z_(3)|=sqrt(2)|z_(1)|

If z_(1)=sqrt(2)((cos pi)/(4)+i sin((pi)/(4))) and z_(2)=sqrt(3)((cos pi)/(3)+i sin((pi)/(3))) then |z_(1)z_(2)|=

If z_(1)=1+i sqrt(3) , z_(2)=1-i sqrt(3), then (z_(1)^(100)+z_(2)^(100))/(z_(1)+z_(2))=

If z_(1) = sqrt(2)(cos""(pi)/(4) + "" i sin""(pi)/(4)) and z_(2) = sqrt(3)(cos""(pi)/(3) + i sin""(pi)/(3)) , then |z_(1)z_(2)| is