1/a+bi =c+di
1a+bi=a−bi(a+bi)(a−bi)=a−bia2+b2.\frac{1}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2+b^2}.a+bi1=(a+bi)(a−bi)a−bi=a2+b2a−bi.
a−bia2+b2=c+di.\frac{a-bi}{a^2+b^2}=c+di.a2+b2a−bi=c+di.
c=aa2+b2.c=\frac{a}{a^2+b^2}.c=a2+b2a.
d=−ba2+b2.d=-\frac{b}{a^2+b^2}.d=−a2+b2b.
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