0 =z2+2iz-1-2i | quadratische Ergänzung
0 = ( z2 + 2iz + i2 - i2 ) - 1 -2i
0 = ( z+i)2 - i2 - 1 - 2i
0 = (z+i)2 + 1 - 1 - 2i
2i = (z+i)2
Nebenrechnung: (1+i)2 = 1 + 2i - 1 = 2i , ebenso (-1-i)2 = (1+i)2 = 2i
2i = (z+i)2
± (1+i) = z+i
- i ± (1+i) = z_(1,2)
z_(1) = - i + 1 + i = 1
z_(2) = -i - (1+i) = - i - 1 - i = -1 -2i
