| ( | 2 | + | 2 | i | ) | ( | 1 | − | 2 | i | ) | = | 0 |
| Left side of the equation = | 2 | ( | 1 | − | 2 | i | ) | + | 2 | i | ( | 1 | − | 2 | i | ) |
| = | 2 | × | 1 | − | 2 | × | 2 | i | + | 2 | i | ( | 1 | − | 2 | i | ) |
| = | 2 | − | 4 | i | + | 2 | i | ( | 1 | − | 2 | i | ) |
| = | 2 | − | 4 | i | + | 2 | i | × | 1 | − | 2 | i | × | 2 | i |
| = | 2 | − | 4 | i | + | 2 | i | − | 4 | i | i |
| = | 2 | − | 2 | i | − | 4 | i | i |
| 2 | − | 2 | i | − | 4 | i | i | = | 0 |
| i2= | 1 2 |