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101.

` 8 - 15 i ` वर्गमूल निकालिये

Answer» `{:( 8 -15 i ),( = ( 1)/(2)[16-30 i] ) ,( = (1)/2[ 5 ^ 2 + (3i)^2 - 2.5. 3i] ) ,( = (1)/(2) (5 -3i) ^ 2 ) , ( therefore sqrt(8-15i) = pm (1)/(sqrt2) ( 5-3i)):} :| {:("Rough"),( (30) /(2) = 15 ) , ( 3"," 5 to 3i"," 5 to 25 + 9 i ^ 2 = 16 ) , ( 1"," 15 to i"," 15 ) , ("real part"= 16 (+ve)),(therefore i " छोटे गुणनखण्ड के साथ ले"):}`
Discussion
102.

सरल कीजिये (Simplify) : ` (( 1 + i ) /(1 - i )) ^( 200) `

Answer» ` ( ( 1 + i ) /( 1 - i )) ^ ( 200) = [ (( 1 + i) ( 1 + i )) /( ( 1 - i ) ( 1 + i)) ] ^ ( 2 00) = [ ((1 + i ) ^ 2 ) /( 1 - i ^ 2 ) ] ^( 200) `
` = (( 1 + i ^ 2 + 2i )/ (2 ) ) ^( 200) = (( 1 - 1 + 2i) /(2))^(200) = (i) ^(200) `
` = (i^ 2 ) ^(100) = ( - 1) ^(100 ) = 1 = 1 + 0.i `
Discussion