Week 3: Complex Numbers – Day 5

Geometry

There are connections between complex numbers and geometry. You can graph complex numbers in the complex plane, where the horizontal axis is the real part, and the vertical coordinate is the complex part. The complex number 2 + 3i, for example, would occupy a point similar to the coordinates (2, 3) in the real plane.

1. Graph the number 1 in the complex plane. (Hint, 1 as a complex number is 1 + 0i, and it occupies a point similar to (1,0) in the real plane). Multiply the number 1 by i and graph the result. Do it again and again. What is the geometrical effect of multiplying by i?

2. Graph the complex number 1 + i in the complex plane. What is the effect of multiplying this number by i? Graph the result.

3. Graph the complex number 2 + i in the complex plane. Multiply this number by the real number 2 and graph the result. What is the effect of multiplying by 2?

4. Graph the complex number -i in the complex plane. Multiply -i by 2 and graph the result. What is the effect of multiplying by 2?

5. Graph the complex number 1 + 2i in the complex plane. Multiply this number by -1 and graph the result. What is the effect of multiplying by -1?

Answers