When a=0, x+I = 0, x =- I don't meet the question.

So a is not equal to 0.

a( 1+I)x2+( 1+a2i)x+a2+I

=ax^2+x+a^2+i(ax^2+a^2x+ 1)

=0

rule

ax^2+x+a^2=0

ax^2+a^2x+ 1=0

a^2= 1

A=- 1 or 1

Discriminant = 1-4a 3 > =0: a =

Discriminant = a4-4a > 0: a > = 2 (2/3) or a

So a < 0

So a=- 1 is the solution of this problem.