1. Chapter 5 Class 11 Complex Numbers
2. Serial order wise

Transcript

Misc 3 Reduce (1/(1 + 4๐)โ2/(1 + ๐)) ((3 โ 4๐)/(5 + ๐)) to the standard form. We have to solve and then make it in Standard form a + ib (1/(1 + 4๐)โ2/(1 + ๐)) ((3 โ 4๐)/(5 + ๐)) = (((1 + ๐) โ 2(1 โ 4๐))/(1 โ 4๐)(1 + ๐) ) ((3 โ 4๐)/(5 + ๐)) = ((1 + ๐ โ 2 + 8๐)/(1 + ๐ โ4๐ โ4๐2)) ((3 โ 4๐)/(5 + ๐)) = ((1 + ๐ โ 2 + 8๐)/(1 + ๐ โ4๐ โ 4 ร(โ1))) ((3 โ 4๐)/(5 + ๐)) = ((1 + ๐ โ 2 + 8๐)/(1 + ๐ โ 4๐ + 4)) ((3 โ 4๐)/(5 + ๐)) = (((1 โ 2) + ๐ + 8๐)/(1 +4 + ๐ โ4๐ )) ((3 โ 4๐)/(5 + ๐)) = ((โ1 + 9๐)/(5 โ 3๐)) ((3 โ 4๐)/(5 + ๐)) = ((โ1 + 9๐) (3 โ 4๐))/(5 โ 3๐)( 5 + ๐) = (โ1(3 โ 4๐) + 9๐(3 โ 4๐))/(5 ( 5 + ๐) โ 3๐( 5 + ๐) ) = (โ3 + 4๐ +27๐ โ36๐2)/(25 + 5๐ โ15๐ โ3๐2) = (โ3 + 4๐ +27๐ โ36 ร โ1)/(25 + 5๐ โ15๐ โ3 ร โ1) = (โ3 + 4๐ +27๐ + 36)/(25 + 5๐ โ15๐ + 3) = (โ3 + 36+ 4๐ +27๐ )/(25 + 3 + 5๐ โ15๐ ) = (33 +31๐ )/(28 โ10๐ ) = (33 +31๐ )/(2(14 โ5๐) ) = 1/2ร(33 +31๐ )/((14 โ5๐) ) Rationalizing = 1/2ร(33 + 31๐ )/((14 โ 5๐) ) ร ((14 + 5i))/((14 + 5i)) = 1/2ร(33(14 + 5i) + 31๐(14 + 5i))/((14 โ 5๐)(14 + 5i)) = 1/2ร(462 + 165๐ + 434๐ + 155๐2)/(142 โ (5๐)2) = 1/2ร(462 + 165๐ + 434๐ + 155๐2)/(196 โ 25๐2) " = " 1/2ร(462 + 165๐ + 434๐ + 155(โ1))/(196 โ25(โ1)) " = " 1/2ร(462 + 165๐ + 434๐ โ 155)/(196 + 25) " = " 1/2ร(462 โ 155 + 165๐ + 434๐ )/221 " = " (307 + 599๐ )/2(221) " = " (307 + 599๐ )/442 = 307/442 + 599/442 ๐ This is the required standard form.