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Lösung 3.1:4b

(Unterschied zwischen Versionen)

Version vom 10:32, 11. Mär. 2009

If we divide both sides by 2−i, we obtain z by itself on the left-hand side,

z=2−i3+2i.

It remains to calculate the quotient on the right-hand side. We multiply top and bottom by the complex conjugate of the denominator,

z=(2−i)(2+i)(3+2i)(2+i)=22−i23

2+3

i+2i

2+2i

i=4+16+3i+4i−2=54+7i=54+57i.

Also, we substitute z=54+57i into the original equation to assure ourselves that we have calculated correctly,

LHS=(2−i)z=(2−i)

54+57i

54+2

57i−i

54−i

57i=58+514i−54i+57=58+7+514−4i=515+510i=3+2i=RHS.