WEBVTT 00:00:00.520 --> 00:00:02.810 现在我们已经看到对 i 00:00:02.810 --> 00:00:06.740 进行幕次越来越高的乘方运算,其结果可能是 1,i, 00:00:06.740 --> 00:00:11.260 -1,-i,然后又回到 00:00:11.260 --> 00:00:12.290 1,i,-1,-i。 00:00:12.290 --> 00:00:14.155 我们现在来做些练习, 00:00:14.155 --> 00:00:15.780 也许就是所谓的难题。 00:00:15.780 --> 00:00:17.110 可能看起来是这样。 00:00:17.110 --> 00:00:18.526 解题时如果你能利用 i 的 00:00:18.526 --> 00:00:22.180 乘方值就在这几个数里循环 00:00:22.180 --> 00:00:23.320 的规律,也是有意思的。 00:00:23.320 --> 00:00:25.990 如果利用这个规律,可以不费力 00:00:25.990 --> 00:00:29.100 就算出 i 的 任意高的次方。 00:00:29.100 --> 00:00:31.650 现在我们先来试一下, 00:00:31.650 --> 00:00:35.310 计算 i 的 100 次方。 00:00:35.310 --> 00:00:39.280 这里关键是 100 是 4 的倍数。 00:00:39.280 --> 00:00:43.800 因此可以说这等同于 i 的 00:00:43.800 --> 00:00:47.467 4 乘以 25 次方。 00:00:47.467 --> 00:00:50.050 而根据指数乘方的性质,它也 00:00:50.050 --> 00:00:55.167 就是 i 的 4 次方的结果的 25 次方。 00:00:55.167 --> 00:00:57.000 00:00:57.000 --> 00:00:59.090 00:00:59.090 --> 00:01:02.300 00:01:02.300 --> 00:01:04.170 00:01:04.170 --> 00:01:05.420 00:01:05.420 --> 00:01:07.390 00:01:07.390 --> 00:01:09.590 00:01:09.590 --> 00:01:12.300 00:01:12.300 --> 00:01:15.910 00:01:15.910 --> 00:01:18.867 00:01:18.867 --> 00:01:20.450 00:01:20.450 --> 00:01:22.672 00:01:22.672 --> 00:01:24.880 00:01:27.730 --> 00:01:31.200 00:01:31.200 --> 00:01:34.620 00:01:34.620 --> 00:01:36.310 00:01:36.310 --> 00:01:38.226 00:01:38.226 --> 00:01:41.500 00:01:41.500 --> 00:01:44.140 00:01:44.140 --> 00:01:45.580 00:01:45.580 --> 00:01:47.050 00:01:47.050 --> 00:01:50.390 00:01:50.390 --> 00:01:56.000 00:01:56.000 --> 00:01:56.960 00:01:56.960 --> 00:01:57.230 00:01:57.230 --> 00:01:58.070 00:01:58.070 --> 00:01:59.840 00:01:59.840 --> 00:02:02.960 00:02:02.960 --> 00:02:05.170 00:02:05.170 --> 00:02:07.920 00:02:07.920 --> 00:02:10.050 00:02:10.050 --> 00:02:11.700 00:02:11.700 --> 00:02:14.760 00:02:14.760 --> 00:02:17.280 00:02:17.280 --> 00:02:21.510 00:02:21.510 --> 00:02:26.150 00:02:26.150 --> 00:02:27.800 00:02:27.800 --> 00:02:31.690 00:02:31.690 --> 00:02:33.130 00:02:33.130 --> 00:02:37.140 00:02:37.140 --> 00:02:39.222 00:02:39.222 --> 00:02:41.430 00:02:41.430 --> 00:02:43.180 00:02:43.180 --> 00:02:46.090 00:02:46.090 --> 00:02:47.620 00:02:47.620 --> 00:02:51.690 00:02:51.690 --> 00:02:55.060 00:02:55.060 --> 00:03:00.450 00:03:00.450 --> 00:03:04.030 00:03:04.030 --> 00:03:06.380 00:03:06.380 --> 00:03:10.250 00:03:10.250 --> 00:03:16.130 00:03:16.130 --> 00:03:19.280 00:03:19.280 --> 00:03:22.180 00:03:22.180 --> 00:03:23.960 00:03:23.960 --> 00:03:25.510 00:03:25.510 --> 00:03:29.340 00:03:29.340 --> 00:03:31.640 00:03:31.640 --> 00:03:33.640 00:03:33.640 --> 00:03:35.920 00:03:35.920 --> 00:03:38.200 00:03:38.200 --> 00:03:45.020 00:03:45.020 --> 00:03:47.540 00:03:47.540 --> 00:03:52.940 00:03:52.940 --> 00:03:55.870 00:03:55.870 --> 00:03:58.870 00:03:58.870 --> 00:04:00.270 00:04:00.270 --> 00:04:02.160 00:04:02.160 --> 00:04:08.020 00:04:08.020 --> 00:04:09.770 00:04:09.770 --> 00:04:12.905 00:04:12.905 --> 00:04:17.240 00:04:17.240 --> 00:04:21.209 00:04:21.209 --> 00:04:24.497 00:04:24.497 --> 00:04:26.080 00:04:26.080 --> 00:04:28.960 00:04:28.960 --> 00:04:33.240 00:04:33.240 --> 00:04:37.287 00:04:37.287 --> 00:04:38.870 00:04:38.870 --> 00:04:41.100 00:04:41.100 --> 00:04:42.600 00:04:42.600 --> 00:04:50.860 00:04:54.030 --> 00:04:56.230 00:04:56.230 --> 00:04:58.860 00:04:58.860 --> 00:05:01.490 00:05:01.490 --> 00:05:02.590 00:05:05.230 --> 00:05:08.930 00:05:08.930 --> 00:05:11.400 00:05:11.400 --> 00:05:14.320 00:05:14.320 --> 00:05:16.840 00:05:16.840 --> 00:05:20.410 00:05:20.410 --> 00:05:23.740 00:05:23.740 --> 00:05:26.850 00:05:26.850 --> 00:05:29.670 00:05:29.670 --> 00:05:32.940 00:05:32.940 --> 00:05:35.630 00:05:35.630 --> 00:05:36.880 00:05:36.880 --> 00:05:39.270 00:05:39.270 --> 00:05:42.480 00:05:42.480 --> 00:05:45.360 00:05:45.360 --> 00:05:48.800 00:05:48.800 --> 00:05:55.340 00:05:55.340 --> 00:05:58.890 00:05:58.890 --> 00:06:01.840 00:06:01.840 --> 00:06:03.450 00:06:03.450 --> 00:06:07.230 00:06:07.230 --> 00:06:09.040 00:06:09.040 --> 00:06:11.920 00:06:11.920 --> 00:06:13.730 00:06:13.730 --> 00:06:15.870 00:06:15.870 --> 00:06:20.530