Considering the one-form $$\alpha=\bar{z}_1dz_1+\bar{z}_2dz_2$$ appeared in this question, I was trying to rewrite this in real coordinates by taking $z_1=x+yi$ and $z_2=z+wi$. So, we have $$\alpha=(x-yi)d(x+yi)+(z-wi)d(z+wi) \\ = xdx+xidy-yidx+ydy+zdz+zidw-widz+wdw.$$ Now, the problem is the terms with $i$. How can I get rid of these terms?
2026-04-03 12:51:04.1775220664
Rewriting a complex differential form in real coordinates
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