1.

निम्नलिखित सम्मिश्र संख्याओं का मापांक ज्ञात कीजिए । (i) `1+sqrt(3)i` (ii) `sqrt(3)+i` (iii) `(1+i)/(1+sqrt(3)i)`

Answer» (i) `|1+sqrt(3)i|=+sqrt(1^(2)(sqrt(3))^(2))=+sqrt(1+3)=+2`
(ii) `|sqrt(3)+i|=+sqrt((sqrt(3))^(2)+1^(2))=+sqrt(3+1)=+2`
(iii) `(1+i)/(1+sqrt(3)i)=(1+i)/(1+sqrt(3)i)xx(1-sqrt(3)i)/(1-sqrt(3)i)`
`=(1+i-sqrt(3)*i+sqrt(3))/(1+3)`
`=(1)/(4)[(sqrt(3)+1)+(1-sqrt(3))i]`
`rArr|(1+i)/(1+sqrt(3)i)|=(1)/(4)|(sqrt(3)+1)+(1-sqrt(3))i|`
`=(1)/(4)sqrt((sqrt(3)+1)^(2)+(1-sqrt(3))^(2))`
`=(1)/(4)sqrt(3+2sqrt(3)+1-2sqrt(3)+3+1)`
`=(1)/(4)sqrt(8)=(1)/(2)sqrt(2)=(1)/(sqrt(2))`


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