A) x²+1=0; 6)x²-8x+65=0.
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A) x²+1=0
This equation does not have any real solutions because x² can never be negative for real numbers x. Therefore, the solutions are complex numbers. By solving x²+1=0, we find that x=±i, where i is the imaginary unit (√-1).

B) x²-8x+65=0
To find the solutions of this equation, we can use the quadratic formula:
x = (-(-8) ± √((-8)² - 4(1)(65))) / 2(1)
x = (8 ± √(64 - 260)) / 2
x = (8 ± √(-196)) / 2
x = (8 ± 14i) / 2
x = 4 ± 7i

Therefore, the solutions to the equation x²-8x+65=0 are x = 4 + 7i and x = 4 - 7i. These are complex numbers.