`(1+2i)/(1-(1-i)^2)`

Express each of the following in the form (a + ib) and find its conjugate: {:((i),(1)/((4+3i)),(ii),(2+3i)^(2),(iii),((2-i))/((1-2i)^(2))),((iv),((1+i)(1+2i))/((1+3i)),(v),((1+2i)/(2+i))^(2),(vi),((2+i))/((3-i)(1+2i))):}

Prove that the matrix A=[[(1+i)/(2),(-1+i)/(2)(1+i)/(2),(1-i)/(2)]] is

If ((1+i)/(1-i))^(2) - ((1-i)/(1+i))^(2) = x + iy then find (x,y).

((1+i)/(1-i))^(2) + ((1-i)/(1+i))^(2) is equal to :

If ((1+i)/(1-i))^(2) - ((1-i)/(1+i))^(2) = x + iy then find (x,y).

((1+i)/(1-i))^(2) + ((1-i)/(1+i))^(2) is equal to :

Given that, z=(1+2i)/(1-i)=((1+2i)(1+i))/((1-i)(1+i))

Simplify : (1+2i)/(1-2i)-(1-2i)/(1+2i)

Simplify : (1+2i)/(1-2i)-(1-2i)/(1+2i)

Perform the following by the indicated operations. Express the result in the form x + iy,where x, y are real numbers i = sqrt(-1) : (2+i)/((1+i)(1-2i)) .