標題:
complex number(f.4)
發問:
我岩岩做左幾題數,但唔知岩唔岩,希望有心知識友可以幫手對下~如果題的話可以俾個詳細D既Process我嗎? Calculate (a)3+i/2-3i + 5-7i/2+3i = 286-208i ? (b)1+2i/3-i - 3+i/2-i = -40i ? (c)2-i/i+3 - i-3/2+i = 50? (d)-5+12i/2+3i + 35+12i/6+i = -6171- 4160i ?
最佳解答:
(a) (3 + i)/(2 - 3i) + (5 - 7i)/(2 + 3i) = (3 + i)(2 + 3i)/(2 - 3i)(2 + 3i) + (5 - 7i)(2 - 3i)/(2 + 3i)(2 - 3i) = (6 + 9i + 2i - 3)/(4 + 9) + (10 - 15i - 14i -21)/(4 + 9) = (3 + 11i)/13 + (-11 - 29i)/13 = (3 + 11i - 11 - 29i)/13 = (-8 - 18i)/13 or -(8/13) - (18/13)i (b) (1 + 2i)/(3 - i) - (3 + i)/(2 - i) = (1 + 2i)(3 + i)/(3 - i)(3 + i) - (3 + i)(2 + i)/(2 - i)(2 + i) = (3 + i + 6i - 2)/(9 + 1) - (6 + 3i + 2i - 1)/(4 + 1) = (1 + 7i)/10 - (5 + 5i)/5 = (1 + 7i)/10 - (10 + 10i)/10 = (1 + 7i - 10 - 10i)/10 = (-9 - 3i)/10 or -(9/10) - (3i/10)i (c) (2 - i)/(i + 3) - (i - 3)/(2 + i) = (2 - i)(i - 3)/(i + 3)(i - 3) - (i - 3)(2 - i)/(2 + i)(2 - i) = (2i - 6 + 1 + 3i)/(-1 - 9) - (2i + 1 - 6 + 3i)/(4 + 1) = (-5 + 5i)/(-10) - (-5 + 5i)/5 = (1 - i)/2 - (-2 + 2i)/2 = (1 - i + 2 - 2i)/2 = (3 - 3i)/2 or (3/2) - (3/2)i (d) (-5 + 12i)/(2 + 3i) + (35 + 12i)/(6 + i) = (-5 + 12i)(2 - 3i)/(2 + 3i)(2 - 3i) + (35 + 12i)(6 - i)/(6 + i)(6 - i) = (-10 + 15i + 24i + 36)/(4 + 9) + (210 - 35i + 72i + 12)/(36 + 1) = (26 + 39i)/13 + (222 + 37i)/37 = (2 + 3i) + (6 + i) = 8 + 4i 2009-09-07 16:50:42 補充： 六呎將軍： 題 (b) 的第一個分母是 3 - i，不是 3 + i。
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