For `Z_1=6sqrt((1-i)/(1+isqrt3)) ; Z_2=6sqrt((1-i)/(sqrt3+i)) ; Z_3=6sqrt((1+i)/(sqrt3-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)|

(sqrt3+i)/(-1-isqrt3)=?

Let z_1=((1+sqrt(3)i)^2(sqrt(3)-i))/(1-i) and z_2=((sqrt(3)+i)^2(1-sqrt(3)i))/(1+i) then

the value of ((1+i sqrt(3))/(1-i sqrt(3)))^(6)+((1-i sqrt(3))/(1+i sqrt(3)))^(6) is

If z = ((1)/(sqrt(3)) + (1)/(2)i)^(7) + ((1)/(sqrt(3))-(1)/(2)i)^(7) , then

The value of ((1+i sqrt(3))/(1-i sqrt(3)))^(6)+((1-i sqrt(3))/(1+i sqrt(3)))^(6)=

The complex number, z=((-sqrt(3)+3i)(1-i))/((3+sqrt(3)i)(i)(sqrt(3)+sqrt(3)i))

The complex number, z=((-sqrt(3)+3i)(1-i))/((3+sqrt(3)i)(i)(sqrt(3)+sqrt(3)i))

The complex number, z=((-sqrt(3)+3i)(1-i))/((3+sqrt(3)i)(i)(sqrt(3)+sqrt(3)i))