Let z = x+5 - 8-2x i where x is a real numberD Find the value of x such that z is an imaginary number

In order for z to be an imaginary number, the real part of z must be zero.

The real part of z is the coefficient of the real unit i, which is (x + 5) - (8 - 2x) = 3x - 3.

Setting this equal to zero, we have 3x - 3 = 0.

Adding 3 to both sides gives 3x = 3, and dividing by 3 gives x = 1.

Therefore, when x = 1, z is an imaginary number.