Rotate point z by angle θ about the origin → z·(cosθ + i sinθ)。
Rotate z by θ about point α → α + (z − α)(cosθ + i sinθ)。
Example ① Find the point obtained by rotating point z=1+i by π/2 about the origin.
Solution:(1+i)·i = i + i² = −1 + i
Solution:(1+i)·i = i + i² = −1 + i
Key Point
- Multiplication by i = a 90° rotation; multiplication by −1 = a 180° rotation
Practice Problems
- Find the point obtained by rotating z=2 by π/3 about the origin.
Answers and Explanations
- Answer:1 + √3 i