To remove the the complex number from the denominator we multiply and divide the entire expression with the conjugate of denominator.
The conjugate of 1 - 4i is 1 + 4i
So, we can write:
[tex] \frac{2+i}{1-4i}* \frac{1+4i}{1+4i} \\ \\
= \frac{2+8i+i-4}{1+16} \\ \\
=\frac{-2+9i}{17} \\ \\
= \frac{-2}{17} + \frac{9i}{17} [/tex]
So, the correct answer is option B
