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

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

Simplify: ((sqrt 3)/2 + i/2)^3

Answer the following. Simplify the following an express in the form a + ib: (5 + 7i) / (4 + 3i) + (5 +7i) / (4 - 3i)

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

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

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 )

Simplify: [ frac{1}{1-2i} + frac{3}{1+i} ] [ frac{3+i}{2-4i} ]

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

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