For
i
=
−
1
i=\sqrt{-1}
i
=
−
1
,
(
3
+
i
)
2
(3+i)^2
(
3
+
i
)
2
= ?
−
9
-9
−
9
8
8
8
8
+
6
i
8+6i
8
+
6
i
6
+
i
6+i
6
+
i
6
+
2
i
6+2i
6
+
2
i
Summary
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Approach
(
3
+
i
)
2
=
(
3
+
i
)
(
3
+
i
)
(3+i)^2 = (3+i)(3+i)
(
3
+
i
)
2
=
(
3
+
i
)
(
3
+
i
)
=
9
+
3
i
+
3
i
+
i
2
= 9 +3i+3i+i^2
=
9
+
3
i
+
3
i
+
i
2
=
9
+
6
i
−
1
= 9+6i-1
=
9
+
6
i
−
1
=
8
+
6
i
= \boxed{8+6i}
=
8
+
6
i