AN EXAMPLE OF GEOMETRY AND

MUTLIPLICATION OF THE COMPLEX NUMBER (0 + i)

WITH EACH POINT IN THE GIVEN TRIANGLE

Complex Plane

1. Multiply (0+i)(1+i) =
                    Graph your answer by changing from (a+bi) to (a, b).

2. Multiply (0+i)(2+i) =
                    Graph your answer by changing from (a+bi) to (a, b).

3. Multiply (0+i)(2+2i) =
                    Graph your answer by changing from (a+bi) to (a, b).

4. Connect the answer points to show how triangular region R has rotated 90 degrees.

5. Multiply each answer complex number point by (0+i) and graph.

6. Multiply each of those answers by (0+i) and graph.

7. What happens if you multiply by (0+i) a fourth time?

8. Multiply: A, B and C, each vertex point's complex number, by some complex number c = a+bi where a^2 + b^2 = 1 and graph your results on another graph page. Find the angle associated with this complex number c. Hint: If a is positive and b is positive then Tan(c's angle) = b/a or c's angle = ArcTan(b/a).

9. Multiply: A, B and C, each vertex point's complex number, by some complex number c = a+bi where a^2 + b^2 not = 1 and graph your results on another graph page. Find the angle associated with this complex number c. Find the magnitude of complex number c where magnitude of c = (a^2 + b^2)^(1/2).

10. Write a few comments giving your conclusions from problem 8 and 9.


Complex Number Addition and Geometry
Complex Number Conjugation and Geometry
Complex Number Arithmetic and Geometry
WT'S MATH COLLECTION

Copyright © 1967 through © 1999 with all rights reserved by William V. Thayer, PedLog