Question

यदि ` [If] z _ 1 = 2 - i , z _ 2 = 1 + i `, ज्ञात कीजिये ` | ( z _ 1 + z _ 2 + 1 ) / ( z _ 1 - z _ 2 + i ) | `

Answer 1

प्रश्न से, ` z _ 1 = 2-i` तथा ` z _ 2 = 1 + i `
अब, ` | ( z _ 1 + z _ 2 + 1 ) /( z _ 1 - z _ 2 + i ) | = | ( 2 - i + 1 + i + 1 ) /( 2 - i - 1 - i + 1 ) | `
` = | ( 4 ) /( 1 - i ) | = | ( 4 ( 1 + i ) ) / (( 1 - i ) ( 1 + i)) | `
` = | ( 4 + 4i) /( 1 - i ^ 2 ) | = | ( 4 + 4i) /( 2 ) | `
` = | 2 + 2 i | = sqrt ( 2 ^ 2 + 2 ^ 2 ) = 2sqrt 2 `