Explore the geometry of complex multiplication. Below, [math]v[/math] and [math]w[/math] are complex numbers, and [math]w=a+bi[/math], where [math]a[/math] and [math]b[/math] are real numbers. Build the product [math]wv[/math] by considering the real and imaginary parts of [math]w[/math] separately. [br][list=1][*]Why is [math]av[/math] as shown? Why is [math]biv[/math] as shown? Why is [math]wv[/math] as shown? [/*][*]Look for similar triangles. Why are they similar? What is the scale factor? [/*][*]How does the angle of the product [math]wv[/math] relate to the angles of [math]w[/math] and of [math]v[/math]? Explain.[/*][*]What about their magnitudes? Explain.[/*][/list]