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

The complex number ((-sqrt(3)+3i)(1-i))/((3+sqrt(3)i)(i)(sqrt(3)+sqrt(3)i)) when represented in the Argand diagram is

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

Consider the complex number z=(5-sqrt3i)/(4+2sqrt3i)

Polar form of the complex number (sqrt(3)+i)/(1-i) is

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

(sqrt(3+4i)+sqrt(3-4i))/(sqrt(3+4i)-sqrt(3-4i))=

The value of ((1+sqrt(3)i)/(1-sqrt(3)i))^(64)+((1-sqrt(3)i)/(1+sqrt(3)i))^(64) is

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

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