Name: Multiplying complex numbers: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 37 s
Description: What is the product (2 + 3i)(4 - i), where i² = -1? Try it, then watch the animated solution.

Multiply like two binomials: each part of

2 + 3i

times each part of

4 - i

. A grid keeps all four.

Fill the grid:

2 \cdot 4 = 8

,

2 \cdot ({-i}) = {-2i}

,

3i \cdot 4 = 12i

,

3i \cdot ({-i}) = {-3i^2}

.

Use

i^2 = {-1}

: the last box is

{-3i^2} = {-3}({-1}) = 3

.

Add the real boxes,

8 + 3 = 11

, and the imaginary boxes,

{-2i} + 12i = 10i

.

Traps:

5 + 10i

uses

i^2 = 1

,

8 - 3i

skips two boxes, and

11 + 14i

loses a minus sign.

Try it first