For
i
=
−
1
i=\sqrt{-1}
i
=
−
1
,
(
2
+
2
i
)
2
(2+2i)^2
(
2
+
2
i
)
2
= ?
−
16
-16
−
16
0
0
0
8
i
8i
8
i
4
+
2
i
4+2i
4
+
2
i
4
+
4
i
4+4i
4
+
4
i
Summary
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Approach
(
2
+
2
i
)
2
=
(
2
+
2
i
)
(
2
+
2
i
)
(2+2i)^2 = (2+2i)(2+2i)
(
2
+
2
i
)
2
=
(
2
+
2
i
)
(
2
+
2
i
)
=
4
+
4
i
+
4
i
+
4
i
2
= 4+4i+4i+4i^2
=
4
+
4
i
+
4
i
+
4
i
2
=
4
+
8
i
−
4
= 4+8i-4
=
4
+
8
i
−
4
=
8
i
= \boxed{8i}
=
8
i