Question

Divide the following complex numbers (2 + i ) ÷ ( 1 - 4i ) ​

Answer 1

-2/17 + 9i/17 fractions

Answer 2

Answer:

- $\frac{2}{17}$ + $\frac{9}{17}$ i

Step-by-step explanation:

Multiply the numerator/denominator by the complex conjugate of the denominator.

The conjugate of 1 - 4i is 1 + 4i

$\frac{(2+i)(1+4i)}{(1-4i)(1+4i)}$ ← expand factors

= $\frac{2+9i+4i^2}{1-16i^2}$ → i² = - 1

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

= $\frac{-2+9i}{17}$

= - $\frac{2}{17}$ + $\frac{9}{17}$ i