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.
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: