Question

hey can you please help me posted picture of question

Answer 1

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:

$\frac{2+i}{1-4i}* \frac{1+4i}{1+4i} \\ \\ = \frac{2+8i+i-4}{1+16} \\ \\ =\frac{-2+9i}{17} \\ \\ = \frac{-2}{17} + \frac{9i}{17}$

So, the correct answer is option B