Show that ` ((1 + i ) /( sqrt2 )) ^( 8) + ((1 - i )/( sqrt2 )) ^( 8) = 2.`

Show that ((1)/( sqrt2) + (i)/( sqrt2 )) ^( 10) + ((1)/( sqrt2 ) - (i)/( sqrt2 )) ^( 10 ) = 0

Show that (1 / sqrt(2) + i / sqrt(2))^10 + (1 / sqrt(2) - i / sqrt(2))^10 = 0 .

Show that (1- 2i )/( 3 - 4i ) + (1 + 2i )/( 3 + 4i ) is real.

Show that (-1 + sqrt (3i))^3 is a real number.

Express the follwing in the form of a + ib, a , b in R i=sqrt ( -1). State the value of a and b. ( - sqrt5 + 2 sqrt ( -4) ) + (1 - sqrt ( -9 ))+ (2 + 3i ) (2 - 3i )

Show that (sqrt(3)/2 + i/2)^3 = i

Show that (frac{1+i}{sqrt 2})^8 + (frac{1-i}{sqrt 2})^8 = 2

Show that (-1+sqrt3 i)^3 is a real number

(1+i)^8 + (1-i)^8 =

Find the value of: (i) (sqrt 3 + 1)^4 - (sqrt 3 - 1)^4 (ii) (2 + sqrt 5)^5 + (2 - sqrt 5)^5