Answer :

[tex] (i-2)^{2} = i^{2} -4i+4 \\ i= \sqrt{-1} \\ i^{2} =-1 \\ i^{2} -4i+4=-1-4i+4=-4i+3\\ answer: 3-4i[/tex]
[tex](i-2)^2=\\--------------------\\use:(a-b)^2=a^2-2ab+b^2\\--------------------\\=i^2-2\times i\times2+2^2=-1-4i+4=3-4i\\\\\\\\i=\sqrt{-1}\Rightarrow i^2=-1[/tex]

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