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计算:(1)(2-i)(-1+5i)(3-4i)+2i;(2)(-12+32i)2-(1-i2)6.

题目详情
计算:
(1)(2-i)(-1+5i)(3-4i)+2i;
(2)(-
1
2
+
3
2
i)2-(
1-i
2
)6.
▼优质解答
答案和解析
(1)(2-i)(-1+5i)(3-4i)+2i
=(-2+i+10i-5i2)(3-4i)+2i
=(3+11i)(3-4i)+2i
=9+33i-12i-44i2+2i
=53+23i;
(2)(-
1
2
+
3
2
i)2-(
1-i
2
)6
=
(
3
i-1)2
4
-[
(1-i)2
2
]3
=
3i2-2
3
i+1
4
-
(1-2i+i2)3
8

=-
1+
3
i
2
-
8i
8

=-
1
2
-
2+
3
2
i.