Solutions to Penrose's ‘Road To Reality’
Chapter 5: Geometry of logarithms, powers, and roots
| §5.1 Geoemtry of complex algebra | ||
| 5.1 | ** | Geometry of complex addition and multiplication (I) |
| 5.2 | ** | Geometry of complex addition and multiplication (II) |
| 5.3 | *** | Complex multiplication as transformation of the complex plane |
| §5.2 The idea of the complex logarithm | ||
| 5.4 | * | Interpretation of the similar-triangle rule |
| §5.3 Multiple valuedness, natural logarithms | ||
| 5.5 | *** | The addition-to-multiplication property of complex exponentiation |
| 5.6 | * | Applications of the Euler formula (I) |
| 5.7 | * | Applications of the Euler formula (II) |
| 5.8 | * | Applications of the Euler formula (III) |
| §5.4 Complex powers | ||
| 5.9 | *** | Multi-valuedness of complex powers (I) |
| 5.10 | *** | Multi-valuedness of complex powers (II) |
| 5.11 | * | Multi-valuedness of the complex logarithm to the base b |
| 5.12 | * | Logarithm of i |
| 5.13 | * | Possible values for ii |
| 5.14 | * | The nth roots of complex numbers |
| 5.15 | ** | The power-to-multiplication property of complex powers |