1. Definition
Multiplying two complex numbers: moduli multiply and arguments add, i.e. rotation and scaling; times i rotates 90° CCW.
2. Formula & Notation
| Modulus, argument | |z|, arg z |
3. Properties & Laws
- |z₁z₂|=|z₁||z₂|;
- arg(z₁z₂)=arg z₁+arg z₂;
- Times i rotates 90°;
- Rotation and scaling.
4. Steps
- Enter two numbers;
- Click "Verify";
- Or click "Load Example".
5. Worked Examples
Example: (1+i)²: modulus 2, argument 90, gives 2i.
6. Common Pitfalls
Arguments add;
Moduli multiply, not add;
Times i rotates.