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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(−i)(2+3i)(−i)z−i(−i)1(−i)=iz2+1−2i+3z−1−i=iz2+(3−2i)z+i.

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

iz2+(3−2i)z+i=iz+23−2i2−23−2i2+i=iz+23−i2−23−i2+i=iz+23−i2−49+3i−i2+i=iz+23−i2−45+4i=iz+23−i2−45i+4i2=iz+23−i2−4−45i.