Multiplying Complex Numbers
- Author:
- Brian Sterr
- Topic:
- Complex Numbers, Numbers
This graph shows how we can interpret the multiplication of complex numbers geometrically.
Given two complex numbers:
, where
Consider their product
Focus on the two right triangles in the diagram:
1 | | Dilate by a scale factor of |
2 | | Rotate by about |
3 | | Dilate by a scale factor of |
4 | | Translate by |
- The right triangle formed by , and the positive real axis.
- The right triangle formed by , and
- The ratio of similitude is , which means that (this is an alternative to the algebraic proof you did for homework)
- The angle formed by , and is congruent to , since they are corresponding angles of similar triangles