Express each one of the following in the standard form `a+ib`,`1/(1-cos theta+2i sin theta)`.

Express each one of the following in the standard form a+ib , (1+2i)^-3

Express each one of the following in the standard form a+ib , (1-i)^3/(1-i^3)

Express each one of the following in the standard form a+ib , (2+i)^3/(2+3i)

Express each one of the following in the standard form a+ib , (3-4i)/((4-2i)(1+i))

Express each one of the following in the standard form a+ib , ((1+i)(1+sqrt (3)i))/(1-i)

Express each one of the following in the standard form a+ib , (3-sqrt(-16)/(1-sqrt(-9)) .

Express each one of the following in the standard form a+ib , ((3-2i)(2+3i))/((1+2i)(2-i)) .

Solve any one of the following sin theta+cos theta=sqrt 2

Find cos^2 theta - sin^2 theta . .

Express the following complex numbers in the standard form a+ib .Also their conjugate. ((1+i)(2+i)/(3+i) .