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Aus Online Mathematik Brückenkurs 2

We start by expanding the quadratic in the numerator,

1+i3(2−i3)2=1+i322−22i3+(i3)2=1+i34−43i−3=1+i31−43i.

Then, we multiply top and bottom by the complex conjugate of the numerator,

1+i31−43i=(1+i3)(1−i3)(1−43i)(1−i3)=12−(i3)211−1i3−43i1+43ii3=1+(3)21−i3−43i+4(3)2i2=1+31−(3+43)i−43=41−12−(1+4)3i=−411−453i.