Example 1.2.14 (a): Multiplying geometrically

Explain geometrically why (1+i)(1-i), i2, and (1+i)4 are all purely real numbers, i.e. the imaginary part of each answer will be zero.
Context Context

Recall that Arg(z) is the principle angle of z. According to our result on multiplication of complex numbers that implies:

Arg(z*w) = Arg(z) + Arg(w)

If we apply that to our vectors we have:

Interactive Complex Analysis, ver. 1.0.0
(c) 2006-2007, Bert G. Wachsmuth
Page last modified: May 29, 2007