Processing Math: Done

Aus Online Mathematik Brückenkurs 2

We complete the square on the left-hand side:

z+12−12+3=0z+12+2=0

Taking the root now gives z+1=i2  i.e. z=−1+i2  and z=−1−i2 .

We test the solutions in the equation to ascertain that we have calculated correctly.

z=−1+i2:z2+2z+3=−1+i22+2−1+i2+3=−12−2i2+i222−2+2i2+3=1−2i2−2−2+2i2+3=0

z=−1−i2:z2+2z+3=−1−i22+2−1−i2+3=−12+2i2+i222−2−2i2+3=1+2i2−2−2−22i+3=0