Find the Value of x for an Imaginary Number z = (x+5) - (8-2x)i

In order for z to be an imaginary number, the real part of z must be zero. \u000A\u000AThe real part of z is the coefficient of the real unit i, which is (x \u002B 5) \u2013 (8 \u2013 2x) \u003D 3x \u2013 3.\u000A\u000ASetting this equal to zero, we have 3x \u2013 3 \u003D 0. \u000A\u000AAdding 3 to both sides gives 3x \u003D 3, and dividing by 3 gives x \u003D 1. \u000A\u000ATherefore, when x \u003D 1, z is an imaginary number.