Simplify: `(1 / i) + (1 / i^2) + (1 / i^3) + (1 / i^4)`

Simplify: [1 / (1 - 2i) + 3 / (1 + i)] [(3 + 4i) / (2 - 4i)]

Simplify (i ^( 65) + (1)/( i ^(45)))

Simplify [ (1)/(1 - 2i ) + (3)/( 1 + i ) ][ ( 3 + 4i )/( 2 - 4i ) ]

If ((1 + i) / (1 - i))^3 - ((1-i) / (1 + i))^3 = x + iy then find x and y.

(Acitity) Express (1)/(i^(1)) + (2)/( i ^(2)) +(3)/( i ^(3)) + (5)/( i ^(4)) in the form of (a + ib).

1 + i^(2n) + i^(4n) + i^(6n)

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

Simplify: i^68 + frac{1}{i^145}

Answer the following. Simplify the following and express in the form a + ib: (1 + 2 / i) (3 + 4 / i) (5 + i)^-1