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Aus Online Mathematik Brückenkurs 2

If we take the minus sign out in front of the whole expression,

−z2+2iz−4z−1 

and collect together the first-degree terms,

−z2+−4+2iz−1 

we can then complete the square of the expression inside the outer bracket

−z2+−4+2iz−1=−z+2−4+2i2−2−4+2i2−1=−z−2+i2−−2+i2−1=−z−2+i2−−22+4i−i2−1=−z−2+i2−4+4i+1−1=−z−2+i2−4+4i=−z−2+i2+4−4i