Name: Dividing complex numbers: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 56 s
Description: For i = sqrt-1, which of the following is equal to 5 + 5i/2 + i? Try it, then watch the animated solution.

To divide by

2 + i

, multiply top and bottom by its conjugate

2 - i

, its mirror image across the real axis.

Bottom:

(2 + i)(2 - i) = 4 - i^2 = 4 + 1 = 5

, the square of the length

\sqrt{5}

.

Top:

(5 + 5i)(2 - i) = 10 - 5i + 10i - 5i^2 = 15 + 5i

, using

i^2 = {-1}

.

Divide each part by

5

:

\tfrac{15 + 5i}{5} = 3 + i

.

Traps:

\tfrac{5}{2} + 5i

splits the bottom,

1 + i

uses

i^2 = 1

,

5 + \tfrac{5}{3}i

has a bottom of

3

.

Try it first