Verified answer

(3+i√5)^2

=(3+i√5)(3+i√5)

=9+6i√(5)+i^1√(25)

=9+6i√(5)-5

=4+6i√(5) answer//

Use FOIL:

(3 + i*sqrt(5))(3 + i*sqrt(5))

= 3^2 + 3*i*sqrt(5) + 3*i*sqrt(5) + 5i^2

= 9 + 6*i*sqrt(5) - 5

= 4 + 6*i*sqrt(5)

= 4 + i*sqrt(180)

= 4 + sqrt(-180)