The equation \(x^2-8x+41=0\) is quadratic equation that requires finding discriminant
\(D=b^2-4ac=(-8)^2-4\cdot 41=64-164=-100.\)
Since discriminant is negative, this equation has two complex roots. Note that \(-1=i^2,\) where \(i\) is imaginary unit. Then \(D=-100=100\cdot (-1)=100\cdot i^2,\\ \\\sqrt{D}=10i.\)
Now the complex roots are
\(x_1=\dfrac{8+10i}{2}=4+5i,\\ \\x_2=\dfrac{8-10i}{2}=4-5i.\)
Answer: correct choice is D.
