1. Definition
(a+bi)(c+di)=(ac−bd)+(ad+bc)i; replace i² by −1.
3. Properties & Laws
- Commutative, associative;
- Times conjugate gives |z|²;
- i²=−1;
- Moduli multiply.
4. Steps
- Enter two numbers;
- Click "Multiply";
- Or click "Load Example".
5. Worked Examples
Example: (3+2i)(1+4i): real −5, imag 14, −5+14i.
6. Common Pitfalls
Real part ac−bd (include −bd);
i²=−1;
Collect terms.