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

Question

asked Apr 28, 2020 137k views

2 Answers

Pion · Answer 1 · 2020-04-29T01:56:51+0000

Answer:

-
(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