Question

सम्मिश्र संख्या `15 (cos 150^(@) +i sin 150^(@))`का सम्मिश्र संख्या `3(cos 60^(@) + i sin 60^(@))`से भागफल ज्ञात कीजिए।

Answer 1

प्रश्नानुसार,
`15 (cos 150^(@) + i sin 150^(@)) div 3(cos 60^(@) + i sin 60^(@))`
`= (15 (cos 150^(@) + i sin 150^(@)))/(3(cos 60^(@) + i sin 60^(@)))`
`= (15 (cos 150^(@) + i sin 150^(@))(cos 60^(@) - i sin 60^(@)))/((cos 60^(@) + i sin 60^(@)) (cos 60^(@) - i sin 60^(@)))`
`= (15(cos 150^(@) cos 60^(@) + sin 150^(@) sin 60^(@)) + i(sin 150^(@) cos 60^(@) - cos 150^(@) sin 60^(@)))/(cos^(2) 60^(@) + sin^(2) 60^(@))`
`=5 [cos (150^(@) - 60^(@)) + i sin (150^(@) -60^(@))]`
`= 5[cos 90^(@) + i sin 90^(@)]`
`=5[0 + i xx 1] = 5i`