Check sibling questions

Misc 3 - Reduce (1/1 + 4i − 2/1 + 𝑖) (3 − 4i/5 + i) - Miscellaneous

Misc 3 - Chapter 5 Class 11 Complex Numbers - Part 2
Misc 3 - Chapter 5 Class 11 Complex Numbers - Part 3

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Misc 3 Reduce (1/(1 + 4 ) 2/(1 + )) ((3 4 )/(5 + )) to the standard form. We have to solve and then make it in Standard form a + ib (1/(1 + 4 ) 2/(1 + )) ((3 4 )/(5 + )) = (((1 + ) 2(1 4 ))/(1 4 )(1 + ) ) ((3 4 )/(5 + )) = ((1 + 2 + 8 )/(1 + 4 4 2)) ((3 4 )/(5 + )) = ((1 + 2 + 8 )/(1 + 4 4 ( 1))) ((3 4 )/(5 + )) = ((1 + 2 + 8 )/(1 + 4 + 4)) ((3 4 )/(5 + )) = (((1 2) + + 8 )/(1 +4 + 4 )) ((3 4 )/(5 + )) = (( 1 + 9 )/(5 3 )) ((3 4 )/(5 + )) = (( 1 + 9 ) (3 4 ))/(5 3 )( 5 + ) = ( 1(3 4 ) + 9 (3 4 ))/(5 ( 5 + ) 3 ( 5 + ) ) = ( 3 + 4 +27 36 2)/(25 + 5 15 3 2) = ( 3 + 4 +27 36 1)/(25 + 5 15 3 1) = ( 3 + 4 +27 + 36)/(25 + 5 15 + 3) = ( 3 + 36+ 4 +27 )/(25 + 3 + 5 15 ) = (33 +31 )/(28 10 ) = (33 +31 )/(2(14 5 ) ) = 1/2 (33 +31 )/((14 5 ) ) Rationalizing = 1/2 (33 + 31 )/((14 5 ) ) ((14 + 5i))/((14 + 5i)) = 1/2 (33(14 + 5i) + 31 (14 + 5i))/((14 5 )(14 + 5i)) = 1/2 (462 + 165 + 434 + 155 2)/(142 (5 )2) = 1/2 (462 + 165 + 434 + 155 2)/(196 25 2) " = " 1/2 (462 + 165 + 434 + 155( 1))/(196 25( 1)) " = " 1/2 (462 + 165 + 434 155)/(196 + 25) " = " 1/2 (462 155 + 165 + 434 )/221 " = " (307 + 599 )/2(221) " = " (307 + 599 )/442 = 307/442 + 599/442 This is the required standard form.

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.