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Aus Online Mathematik Brückenkurs 2

A quotient of two complex numbers is calculated by multiplying the top and bottom of the fraction by the complex conjugate of the denominator,

1+i3−2i=1+i3−2i1−i1−i.

Then, the formula for the difference of two squares gives that the new denominator is a real number,

1+i3−2i1−i1−i=(1+i)(1−i)(3−2i)(1−i)=12−i2(3−2i)(1−i)=1+1(3−2i)(1−i)=2(3−2i)(1−i).

All that remains is to multiply together what is in the numerator,

2(3−2i)(1−i)=231−3i−2i1−2i(−i)=23−3i−2i+2i2=23−(3+2)i+2(−1)=21−5i=21−25i.