Processing Math: Done

Aus Online Mathematik Brückenkurs 2

Before we can complete the square of the expression, we need to take out the factor i in front of z2

iz2+i2+3iz−i1 

Then, simplify the complex fractions by multiplying top and bottom by −i (the denominator's complex conjugate):

iz2+i−i2+3i−iz−i−i1−i=iz2+1−2i+3z−1−i=iz2+3−2iz+i

Now we are ready to complete the square of the second-degree expression inside the bracket:

iz2+3−2iz+i=iz+23−2i2−23−2i2+i=iz+23−i2−23−i2+i=iz+23−i2−49+3i+1+i=iz+23−i2−45+4i=z+23−i2−45i+4i2=z+23−i2−4−45i