Argand diagram transformations

<p>Can you connect this with our method of complex division? That is, re-examine the following:</p>
<p>\[\begin{aligned} \frac{z}{w} &= \frac{x+iy}{u+iv} \\ &= \frac{x+iy}{u+iv} \cdot \frac{u-iv}{u-iv} \\ &= \frac{(x+iy)(u-iv)}{(u+iv)(u-iv)} \\ &= \frac{(xu+yv)+i(yu-xv)}{u^2-(iv)^2} \\ &= \frac{(xu+yv)+i(yu-xv)}{u^2+v^2} \end{aligned}\]</p>

Can you connect this with our method of complex division? That is, re-examine the following:

\[\begin{aligned} \frac{z}{w} &= \frac{x+iy}{u+iv} \\ &= \frac{x+iy}{u+iv} \cdot \frac{u-iv}{u-iv} \\ &= \frac{(x+iy)(u-iv)}{(u+iv)(u-iv)} \\ &= \frac{(xu+yv)+i(yu-xv)}{u^2-(iv)^2} \\ &= \frac{(xu+yv)+i(yu-xv)}{u^2+v^2} \end{aligned}\]

Modulus, Argument, and Operations on Complex Numbers

Complex Numbers

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Remark connecting complex division

Remark connecting complex division