Respuestas
Es solo las que me faltaron porque no me dejó poner todas otra vez (exceso de caracteres)
166. (-2 - 2i)³ =
(-2 - 2i)(-2 - 2i)(-2 - 2i) =
(4 + 4i + 4i + 4i²)(-2 - 2i) =
(4 + 8i + 4i²)(-2 - 2i) =
-8 - 8i - 16i - 16i² - 8i² - 8i³ =
-8i³ - 24i² - 24i - 8
167. (-2 + 3i)³ =
(-2 + 3i)(-2 + 3i)(-2 + 3i) =
(4 - 6i - 6i + 9i²)(-2 + 3i) =
(4 - 12i + 9i²)(-2 + 3i) =
-8 + 12i + 24i - 36i² - 18i² + 27i³ =
27i³ - 54i² + 36i - 8
168. (4 - i)³ =
(4 - i)(4 - i)(4 - i) =
(16 - 4i - 4i + i²)(4 - i) =
(16 - 8i + i²)(4 - i) =
64 - 16i - 32i + 8i² + 4i² - i³ =
-i³ + 12i² - 48i + 64
169. (-4 - 2i)³ =
(-4 - 2i)(-4 - 2i)(-4 - 2i) =
(16 + 8i + 8i + 4i²)(-4 - 2i) =
(16 + 16i + 4i²)(-4 - 2i) =
-64 - 32i - 64i - 32i² - 16i² - 8i³ =
- 8i³ - 48i² - 96i - 64 =
-8 ( i³ - 6i² - 12i - 8)
170. (2 - 2i)³ =
(2 - 2i)(2 - 2i)(2 - 2i) =
(4 - 4i - 4i + 4i²)(2 - 2i) =
(4 - 8i + 4i²)(2 - 2i) =
8 - 8i - 16i + 16i² + 8i² - 8i³ =
- 8i³ + 24i² - 24i + 8 =
-8 (i³ - 3i² + 3i - 1)
171. (1 + i)⁴ =
(1 + i)(1 + i)(1 + i)(1 + i) =
(1 + i + i + i²)(1 + i + i + i²) =
(1 + 2i + i²)(1 + 2i + i²) =
1 + 2i + i² + 2i + 4i² + 2i³ + i² + 2i³ + i⁴ =
i⁴ + 4i³ + 6i² + 4i + 1
172. (1 - i)⁴ =
(1 - i)(1 - i)(1 - i)(1 - i) =
(1 - i - i + i²)(1 - i - i + i²) =
(1 - 2i + i²)(1 - 2i + i²) =
1 - 2i + i² - 2i + 4i² - 2i³ + i² - 2i³ + i⁴ =
i⁴ - 4i³ + 6i² - 4i + 1
173. (1 + 2i)⁴ =
(1 + 2i)(1 + 2i)(1 + 2i)(1 + 2i) =
(1 + 2i + 2i + 4i²)(1 + 2i + 2i + 4i²) =
(1 + 4i + 4i²)(1 + 4i + 4i²) =
1 + 4i + 4i² + 4i + 16i² + 16i³ + 4i² + 16i³ + 16i⁴ =
16i⁴ + 32i³ + 24i² + 8i + 1
174. (3 + i)⁴ =
(3 + i)(3 + i)(3 + i)(3 + i) =
(9 + 3i + 3i + i²)(9 + 3i + 3i + i²) =
(9 + 6i + i²)(9 + 6i + i²) =
81 + 54i + 9i² + 54i + 36i² + 6i³ + 9i² + 6i³ + i⁴ =
i⁴ + 12i³ + 54i² + 108i + 81
175. (2 - i)⁴ =
(2 - i)(2 - i)(2 - i)(2 - i) =
(4 - 2i - 2i + i²)(4 - 2i - 2i + i²) =
(4 - 4i + i²)(4 - 4i + i²) =
16 - 16i + 4i² - 16i + 16i² - 4i³ + 4i² - 4i³ + i⁴ =
i⁴ - 8i³ + 24i² - 32i + 16
176. (1 - i)⁵ =
(1 - i)(1 - i)(1 - i)(1 - i)(1 - i) =
(1 - i - i + i²)(1 - i - i + i²)(1 - i) =
(1 - 2i + i²)(1 - 2i + i²)(1 - i) =
(1 - 2i + i² - 2i + 4i² - 2i³ + i² - 2i³ + i⁴)(1 - i) =
(1 - 4i + 6i² - 4i³ + i⁴)(1 - i) =
1 - 4i + 6i² - 4i³ + i⁴ - i + 4i² - 6i³ + 4i⁴ - i⁵ =
-i⁵ + 5i⁴ - 10i³ + 10i² - 5i + 1
177. (2 + i)⁵ =
(2 + i)(2 + i)(2 + i)(2 + i)(2 + i) =
(4 + 2i + 2i + i²)(4 + 2i + 2i + i²)(2 + i) =
(4 + 4i + i²)(4 + 4i + i²)(2 + i) =
(16 + 16i + 4i² + 16i + 16i² + 4i³ + 4i² + 4i³ + i⁴)(2 + i) =
(16 + 32i + 24i² + 8i³ + i⁴)(2 + i) =
32 + 64i + 48i² + 16i³ + 2i⁴ + 16i + 32i² + 24i³ + 8i⁴ + i⁵ =
i⁵ + 10i⁴ + 40i³ + 80i² + 80i + 32
178. (1 + 2i)⁵ =
(1 + 2i)(1 + 2i)(1 + 2i)(1 + 2i)(1 + 2i) =
(1 + 2i + 2i + 4i²)(1 + 2i + 2i + 4i²)(1 + 2i) =
(1 + 4i + 4i²)(1 + 4i + 4i²)(1 + 2i) =
(1 + 4i + 4i² + 4i + 16i² + 16i³ + 4i² + 16i³ + 16i⁴)(1 + 2i) =
(1 + 8i + 24i² + 32i³ + 16i⁴)(1 + 2i) =
1 + 8i + 24i² + 32i³ + 16i⁴ + 2i + 16i² + 48i³ + 64i⁴ + 32i⁵ =
32i⁵ + 80i⁴ + 80i³ + 40i² + 10i + 1
179. (1 - i)⁶ =
(1 - i)(1 - i)(1 - i)(1 - i)(1 - i)(1 - i) =
(1 - i - i + i²)(1 - i - i + i²)(1 - i - i + i²) =
(1 - 2i + i²)(1 - 2i + i²)(1 - 2i + i²) =
(1 - 2i + i² - 2i + 4i² - 2i³ + i² - 2i³ + i⁴)(1 - 2i + i²) =
(1 - 4i + 6i² - 4i³ + i⁴)(1 - 2i + i²) =
1 - 4i + 6i² - 4i³ + i⁴ - 2i + 8i² - 12i³ + 8i⁴ - 2i⁵ + i² - 4i³ + 6i⁴ - 4i⁵ + i⁶ =
1 - 4i + 6i² - 2i =
i⁶ - 6i⁵ + 15i⁴ - 20i³ + 15i² - 6i + 1
180. (2 - i)⁶ =
(2 - i)(2 - i)(2 - i)(2 - i)(2 - i)(2 - i) =
(4 - 2i - 2i + i²)(4 - 2i - 2i + i²)(4 - 2i - 2i + i²) =
(4 - 4i + i²)(4 - 4i + i²)(4 - 4i + i²) =
(16 - 16i + 4i² - 16i + 16i² - 4i³ + 4i² - 4i³ + i⁴)(4 - 4i + i²) =
(16 - 32i + 24i² - 8i³ + i⁴)(4 - 4i + i²) =
64 - 64i + 16i² - 128i + 128i² - 96i³ + 32i⁴ - 4i⁵ + 16i² - 32i³ + 24i⁴ - 8i⁵ + i⁶ =
64 - 64i - 128i =
i⁶ - 12i⁵ + 60i⁴ - 128i³ + 160i² - 192i + 64