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इन सम्मिश्र संख्याओं का मापांक तथा मुख्य कोणाक ज्ञात कीजिये | ` ( 5 ) /(2) ( cos 300^@ + i sin 30 ^@) `

Answer» ` z = ( 5 ) / ( 2 ) ( cos 300^ @ + i sin 30 ^@ ) = ( 5 ) /(2) ( cos ( 360 ^@ - 60 ^@ ) + i. ( 1 ) / ( 2 ) ) `
` = ( 5 ) /(2) ( cos 60 ^@ + i. ( 1 ) / ( 2 ) ) `
` = ( 5 ) / ( 2 ) ( ( 1 ) / (2 ) + i . ( 1 ) / (2 ) ) = ( 5 ) / ( 2 sqrt2 ) (( 1 ) /( sqrt 2 ) + i. ( 1 ) / ( sqrt 2 ) ) `
` = ( 5 ) /( 2sqrt 2 ) ( cos "" ( pi ) / ( 4 ) + i sin "" ( pi ) / ( 4 )) `
` therefore |z| = ( 5 ) / ( 2sqrt 2 ) ` तथा arg z कोणाक का मुख्य मान ` z = ( pi ) /( 4 ) ( because ( pi ) / ( 4 ) in ( - pi , pi ) ) `


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