Question 359079
then (a+bi)*(a+bi) = 8i = a^2-b^2+2abi
 
hence a=+/-b, and 
 
 2ab=8, implies a=b, and 2a^2=8, a^2=4, a=+/-2=b
 
 
we have 2 solutions : (2+2i) and -(2+2i). 
 
Verification : (2+2i)(2+2i)=4+4i+4i-4=8i