1. If A is a real number and you are seeking for the solutions in real numbers then
A^4+2=11 ---> A^4 = 11-2 ---> A^4 = 9 ---> A^2 = ---> A^2 = 3 ---> A = +/- .
Two solutions.
2. If A is a complex number and you are seeking for the solutions in complex numbers then
A^4+2=11 ---> A^4 = 11-2 ---> A^4 = 9 ---> A^2 = +/- ---> A^2 = +/- 3 ---> A = , or A = , or A = , or A = .
Four solutions.