Lösung 3.3:5b

Aus Online Mathematik Brückenkurs 2

Complete the square of the left-hand side:

z−22−i2−22−i2+3−i=0z−22−i2−1−i+41i2+3−i=0z−22−i2−1+i+41+3−i=0z−22−i2+49=0

Taking the root then gives that the solutions are

z−22−i=23iz=1+i1−2i  

Finally, we substitute the solutions into the equation and check that it is satisfied:

z=1+i:z2−2−iz+3−i=1+i2−2−i1+i+3−i=1+2i+i2−2+2i−i−i2+3−i=1+2i−1−2−i−1+3−i=0

z=1−2i:z2−2−iz+3−i=1−2i2−2−i1−2i+3−i=1−4i+4i2−2−4i−i+2i2+3−i=1−4i−4−2+5i+2+3−i=0