Complex Numbers

Question

Find the product of the two numbers, (7+2i) and (3+5i). Plot this point on your graph and find the magnitude and direction of the product.

a. What relationship do you notice between the magnitude of the product and the magnitude of the original numbers? Is this relationship true if one of the numbers is not in the first quadrant? Test more points as necessary.

b. What relationship do you notice between the directions of your original numbers and the product? Test more points as necessary.

Answer 1

All you need to remember when you're multiplying out the two complex numbers is that i² = -1. Other than that, multiplying it out is simply a matter of multiplying out two binomials, which you should know how to do.

The magnitude of a complex number (a + bi) is simply √a²+b²

The direction of a complex number (a+bi) (which I'm assuming they want the angle) is just tan (b/a).

The rest is something you need to experiment with and figure out.