sendo Z=2-2i, calcule:a) Z²b)Z (elevado a 8)c) Z (elevado a 9).... Pergunta de ideia deGPB

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sendo Z=2-2i, calcule:
a) Z²
b)Z (elevado a 8)
c) Z (elevado a 9)

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Celio

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Olá, GPB.

$z=2-2i\\\\ a) z^2=(2-2i)^2=4-8i+4i^2=4-8i+4(-1)=-8i\\\\ b)z^8=(z^2)^4=(-8i)^4=4096i^4=4096i^2\cdot i^2=4096(-1)(-1)=\\4096\\\\ c) z^9=z^8 \cdot z=4096(2-2i)=8192-8192i$

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