3. Példa ${1+2i\over {1-2i}} =?$

Megoldás.

${1+2i\over{1-2i}}={1+2i\over{1-2i}}\cdot{1+2i\over{1+2i}}={(1+2i)^2\over{1^2+2^2}}={-3+4i\over5}=-{3\over5}+{4\over5}i$