Find the real numbers x and y such that `frac{x}{1+2i}` + `frac{y}{3+2i}` = `frac{5+6i}{-1+8i}`

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

Show that frac{1-2i}{3-4i} + frac{1+2i}{3+4i} is a real

Find the value of: x^3 + x^2 -x+22, if x= frac{5}{1-2i}

(-frac{1}{2}+frac{sqrt3}{2}i)^1000 =

Find the value of x and y which satisfy the following equation (x, y in R): frac{x+iy}{2+3i} + frac{2+i}{2-3i} = frac{9}{13} (1+i)

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

( i^57 + frac{1}{i^25} ) =

Find the modulus of [ frac{1+i}{1-i} - frac{1-i}{1+i} ]

The modulus of frac{1-i}{3+i}+frac{4i}{5} is

(frac{1+i}{1-i})^2 =?