web analytics

Ex 5.1, 8 - Express in a + ib: (1 - i)4 - Chapter 5 Class 11 - Ex 5.1

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

Transcript

Ex5.1, 8(Method 1) Express the given Complex number in the form a + ib: (1 โ€“ ๐‘– )4 (1 โ€“ ๐‘–)4 = ((1 โ€“ ๐‘–)^2 )^2 = ( 1 โ€“ ๐‘– )2 (1 โ€“ ๐‘– )2 Using ( a โ€“ b ) 2 = a 2 + b 2 โ€“ 2ab = ( 12 + ๐‘– 2 โ€“ 2 ร— 1 ร— ๐‘– ) ( 12 + ๐‘– 2 โ€“ 2 ร— 1 ร— ๐‘– ) = ( 1 + ๐‘– 2 โ€“ 2 ๐‘– ) ( 1 + ๐‘– 2 โ€“ 2 ๐‘– ) = ( 1 โˆ’ 1 โ€“ 2 ๐‘– ) ( 1 โˆ’1 โ€“ 2 ๐‘– ) = (0 โ€“ 2 ๐‘– ) ( 0 โ€“ 2 ๐‘– ) = ( โˆ’2 ๐‘– ) (โˆ’ 2 ๐‘– ) = 4 ๐‘– 2 Putting i 2 = โˆ’ 1 = 4 ร— โ€“1 = โ€“ 4 = โ€“ 4 + 0 = โ€“ 4 + 0๐‘– Ex5.1, 8(Method 2) Express the given Complex number in the form a + ib: (1 โ€“ i )4 (1 โ€“ ๐‘– ) 4 = ((1 โ€“ ๐‘–)^2 )^2 Using ( a โ€“ b ) 2 = a 2 + b 2 โ€“ 2ab = ( 1 + ๐‘– 2 โ€“ 2 ร— 1 ร— ๐‘– )2 = ( 1 + ๐‘– 2 โ€“ 2 ๐‘– )2 Putting i 2 = โˆ’ 1 "= "( 1 + (โˆ’ 1) โ€“ 2 ๐‘– ) 2 "=" ( 1 โˆ’ 1 โ€“ 2 ๐‘– )2 "=" (0 โ€“ 2 ๐‘– ) 2 "=" ( โˆ’2 ๐‘– )2 "=" ( โˆ’ 2 )2 ร— ๐‘– 2 = ( โˆ’ 2 ร— โˆ’ 2 ) ร— ( โˆ’ 1 ) = 4 ร— ( โˆ’ 1 ) = โ€“ 4 = โ€“ 4 + 0 = โ€“ 4 + 0๐‘–

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
Jail