Find the value of: `((1 + isqrt(3)) / (1 - isqrt(3)))^6 + ((1 - isqrt(3)) / (1 + isqrt(3)))^6` using De Moivre's Theorem

Show that (sqrt(7) + isqrt(3)) / (sqrt(7) - isqrt(3)) + (sqrt(7) - isqrt(3)) / (sqrt(7) + isqrt(3)) , is real.

Find the value of (1 + i)^(2 / 3) using De Moivre's Theorem.

The value of [frac{1+isqrt3}{1-isqrt3}]^6 + [frac{1-isqrt3}{1+isqrt3}]^6 is

FInd the expansion of (6-3x)^(-1/3)

Find the value of the determinants: A=|{:(5, 3),(3,1):}|

If z = frac{1-isqrt3}{1+isqrt3} , then arg(z) =

If [frac{1+isqrt3}{1-isqrt3}]^n is a integer, then n is

Select and write the correct answer from the given alternatives in each of the following: (sqrt(3) + isqrt(2)) (sqrt(2) + isqrt(3)) =

Find n if. (n) / (8!) = 3 / (6!) + 1 / (4!)