\(i = \sqrt{-1}\)
\(i^2=-1, \ i^3=i^2, i=-i,\)
\(i^4=i^3, i=-i, i=1,.., i^{4n}=1\)
\(i^{4n+1}=i, i^{4n+2}=-1, i^{4n+3}=-i\)
\((a+bi)+(c+di)=(a+c)+(b+d)i\)
\((a+bi)-(c+di)=(a-c)+(b-d)i\)
\((a+bi)(a-bi)=a^2+b^2\)
\((a+bi)(c+di)=(ac-bd)+(ad+bc)i\)
\(\dfrac{a+bi}{c+di}= \dfrac{a+bi}{c+di}, \dfrac{c-di}{c-di}= \dfrac{ac+bd}{c^2+d^2}+(\dfrac{bc-ad}{c^2+d^2})i\)
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