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Lösung 3.1:2a

(Unterschied zwischen Versionen)

Version vom 10:30, 11. Mär. 2009

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+i3−2i

1−i1−i.

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

1+i3−2i

1−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)=23

1−3

i−2i

1−2i

(−i)=23−3i−2i+2i2=23−(3+2)i+2

(−1)=21−5i=21−25i.