`((-1-i)/(sqrt(2)))^(100)` equals

((1+i)/(sqrt(2)))^(8)+((1-i)/(sqrt(2)))^(8) is equal to

((1+i)/(sqrt(2)))^8+((1-i)/(sqrt(2)))^8 is equal to

((1+sqrt(3)i)/(1-sqrt(3)i))^(181) + ((1-sqrt(3)i)/(1+sqrt(3)i))^(181) is equal to ______________

Show that ((-1+sqrt(3)i)/(2))^(n)+((-1-sqrt(3i))/(2))^(n) is equal to 2 when n is a multiple of 3 and 3 is equal to -1 when n is any other positive integer.

What is ((sqrt(3)+i)/(sqrt(3)-i))^(6) equal to, where I = sqrt(-1) ?

Write the comple number in a + ib form unsing cube roots of unity: (a) (-(1)/(2) + sqrt(3)/(2)i)^(1000) (b)If z =(sqrt(3) + i)^(17)/((1-i)^(50)) (c) (i + sqrt(3))^(100) + (i+ sqrt(3))^(100) + 2^(100)