Lösung 3.1:2a

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 conjugate rule 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−12i−2i(−i)=23−3i−2i+2i2=23−(3+2)i+2(−1)=21−5i=21−25i