Return to the complex multiplication overview.
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:
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`.
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Update History:18 October 2016: Created this page.