Tiêu đề Complex Number Varsity Practice Sheet ‍Solution.pdf ✅

RwUj msL ̈v  Varsity Practice Sheet 1 03 RwUj msL ̈v Complex Number 1. 1 + 2i RwUj msL ̈vi Ae ̄’vb ev ̄Íe Aÿ n‡Z KZ `~‡i? 1 2 i 1 + 2 DËi: 2 e ̈vL ̈v: (1 + 2i)  (1, 2 ) 2 KvíwbK ev ̄Íe (1, 2) ● 2. g~jwe›`y n‡Z – 1 + 3i Gi `~iZ¡ KZ? 3 2 1 4 DËi: 2 e ̈vL ̈v: ● ● O(0,0) (–1  3) – 1 + 3i  (–1, 3 )  g~jwe›`y n‡Z `~iZ¡ = 1 2 + ( 3) 2 = 2 3. 3 I – 4i we›`y `ywUi ms‡hvMKvix †iLvi •`N© ̈ wbY©q Ki| 5 7 8 10 DËi: 5 e ̈vL ̈v: 3 I – 4i we›`yi ms‡hvMKvix †iLvi •`N© ̈ n‡e |z1 – z2| = |3 + 4i| [z1 = 3 ; z2 = – 4i] = 3 2 + 42 = 5 4. – 1 – i I 2 + 3i we›`y `ywUi ms‡hvMKvix †iLvi •`N© ̈ †ei Ki| 3 5 6 None DËi: 5 e ̈vL ̈v: z1 = – 1 – i I z2 = 2 + 3i ms‡hvMKvix †iLvi •`N© ̈ = |z1 – z2| = |– 3 – 4i| = 3 2 + 42 = 5 5. z = – 2i n‡j, – z Gi cÖwZiƒcx we›`y †KvbwU? (–2, 0) (0, – 2) (2, 0) (0, 2) DËi: (0, 2) e ̈vL ̈v: – z = 2i = 0 + 2i cÖwZiƒcx we›`y(x, y)  (0, 2) 6. z GKUv m¤ú~Y© ev ̄Íe msL ̈v Ges z Gi ev ̄Íe Ask – 2 n‡j, z Gi Ae ̄’vbÑ FYvZ¥K Y A‡ÿ abvZ¥K X A‡ÿ (– 2, 0) we›`y‡Z (2, 0) we›`y‡Z DËi: (– 2, 0) we›`y‡Z e ̈vL ̈v: z = x + iy = – 2 + 0.i [m¤ú~Y© ev ̄Íe e‡j, y = 0 ; x = – 2]  we›`y (– 2, 0) 7. 1 + i, i – 1, 2i Øviv MwVZ wÎfz‡Ri AvM©Û wP‡Î †ÿÎdj = ? 1 2 1 2 2 DËi: 1 e ̈vL ̈v: wZbwU kxl©we›`y, A (1, 1), B (– 1, 1), C (0, 2)  = 1 2       1 – 1 0 1 1 2 1 1 1 = 1 2 |1 (1 – 2) – 1 (– 1) + 1 (– 2)| = 1 2 | – 1 + 1 – 2| = 1 2 |– 2| = 1 8. 1 + 2i 1 – i †Kvb PZzf©v‡M Ae ̄’vb K‡iÑ 1 st 2 nd 3 rd 4 th DËi: 2 nd e ̈vL ̈v: z = (1 + 2i) (1 + i) (1 – i) (1 + i) = – 1 + 3i 2 = – 1 2 + 3 2 i hv 2 nd PZyf©v‡M Aew ̄’Z| 9. a + ib = 0 n‡j †KvbwU mZ ̈? †hLv‡b a,b I R a = 0; b  0 a = 0; b = 0 a  0; b = 0 None DËi: a = 0; b = 0 e ̈vL ̈v: a + ib = 0 n‡e hLb a I b DfqB 0 nq| 10. n  N n‡j i 8n + 5 Gi gvb KZ? 1 –1 i – i DËi: i e ̈vL ̈v: i 4n = 1 GLb, i 8n+5 = i8n . i5 = (i4n) 2 . i5 = i A_ev, n = 1 a‡i cvB i 8n + 5 = i13 = i