Technologically Embodied
Geometric Functions
Complex Multiplication Part 4: Multiply Two Complex Numbers

In this activity you will investigate the multiplication of two complex numbers v and w using a combination of algebra and geometry. First, remember that you can express w as w=(x_w + i*y_w).

Using this formula for w, you can use the distributive property to write v*w = v*(x_w + i*y_w) = v*x_w + v*i*y_w.

In this expanded form, x_w and y_w are both real numbers. This enables you to use geometry on the complex plane to multiply the complex numbers v·w, based on three geometric techniques to:

• geometrically multiply a complex number by i (to construct v*i), and
• geometrically multiply a complex number by a real number (to construct v*x_w and v*i*y_w),
• geometrically add two complex numbers (to construct the sum v*x_w + v*i*y_w).

On pages 1–3, you'll review these three techniques.

On page 4 you'll use the techniques to multiply two complex numbers v and w, and you'll investigate the geometric relationships connecting the complex numbers v, w, and v·w.

X

Release Information and Rights

Update History: