If the expression `(1 + ir)^3` is of the form of `s(1+ i)` for some real 's' where 'r' is also real and `i = sqrt(-1)`

If the expression (-3 I ^(2) + 2i )/(2 +i) is written in the form a + bi, where a and b are real numbers and I = sqrt-1, what is the value of a ?

Express each of the following in the form b or bi, where b is a real number sqrt((-1)/(3))

If z=2-3i, express (1-2z)/(z-3) in the form A+iB where A and B are real.

Express ((1+i)/(1-i))^(3) in the form A + iB (A and B are real numbers).

Express each of the following in the form b or bi, where b is a real number (1)/(2) sqrt((-3)/(4))

( 8 - i)/( 3 - 2i ) If the expression above is rewritten in the form a + bi , where a and b are real numbers, what is the value of a ? ( Note : i=sqrt ( -1) )

Perform the indicated operation and give your answer in the form x + iy, where x and y are real numbers and i = sqrt (-1) . (1/2+1/4i)(-2/3-1/4i) .

Perform the indicated operation and give your answer in the form x+yi , where x and y are real numbers and i= sqrt(-1) (5+2i)/(-1+sqrt3i)

Perform the indicated operation and give your answer in the form x + iy, where x and y are real numbers and i = sqrt (-1) . (5+2i)/(-1+sqrt 3 i) .

Perform the following by the indicated operations. Express the result in the form x + iy,where x, y are real numbers i = sqrt(-1) : ((1-i)(2-i)(3-i))/(1+i) .