Question

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

Answer 1

-
`(2)/(17)` +
`(9)/(17)` i

Explanation:

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

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

`((2+i)(1+4i))/((1-4i)(1+4i))` ← expand factors

=
`(2+9i+4i^2)/(1-16i^2)` → i² = - 1

=
`(2+9i-4)/(1+16)`

=
`(-2+9i)/(17)`

= -
`(2)/(17)` +
`(9)/(17)` i

Answer 2

-2/17 + 9i/17 fractions