` sqrt 2 - sqrt 2 i` का संयुग्मी, मापांक तथा कोणाक निकालिये |

Explanation

माना कि ` z = sqrt2 - sqrt 2 i `, यहाँ ` x = sqrt2 , y = -sqrt 2 `
` bar z = bar (sqrt 2 - sqrt 2 ) i = sqrt2 + sqrt 2 i" " `[ ` barz ` की परिभाषा से ]
तथा ` |z| = | sqrt 2 - sqrt 2 i | = sqrt ( ( sqrt 2) ^ 2 + ( sqrt 2 ) ^ 2) = sqrt ( 2 + 2 ) = 2 `
Argument of z : ` tan theta = | ( y ) /( x )| = | ( - sqrt 2 ) /( sqrt 2 ) | = 1 = tan 45 ^@ therefore theta = ( pi ) /( 4 ) , 0 le theta le ( pi )/ ( 2 ) `
` because x = sqrt 2 gt 0 ` तथा ` y = - sqrt 2 lt 0 ` अतः z चतुर्थ पाद में होगा |
` therefore arg = z = 2pi - theta = 2 pi - ( pi ) /( 4 ) = ( 7pi ) /( 4 ) `
Note arg z का principal value भी लिखा जा सकता है |
Principal value of arg z ` = ( 7 pi ) /(4 ) - 2pi = - ( pi ) / ( 4 ) `