Question

यदि ` (If) |z _ 1 | = | z _ 2 | = 1 ` तो साबित कीजिये कि
` | z _ 1 + z _ 2| = | ( 1 ) / ( z _ 1 ) + ( 1 ) / ( z _ 2 ) | `

Answer 1

` because | z _ 1 | = 1 rArr | z _ 1 | ^ 2 = 1 rArr z _ 1 bar z _ 1 = 1 rArr ( 1 ) /( z _ 1 ) = bar z _ 1 `
इसी तरह ` |z _ 2 | = 1 rArr | z _ 2 | ^ 2 = 1 rArr z_ 2 bar z _ 2 = 1 rArr ( 1 ) / ( z _ 2 ) = bar z _ 2 `
अब ` | ( 1 ) / ( z _ 1 ) + ( 1 ) /( z _ 2 ) | = | bar z _ 1 + bar z _ 2 | = bar ( | z _ 1 + z _ 2 | ) [ because bar ( z _ 1 + z _2 ) = bar z _1 + bar z _ 2 ] `
` = |z _ 1 + z _ 2 |" " [ because |bar z| = |z|]`