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Find the value of |(1+i)((2+i))/((3+i))|...

Find the value of `|(1+i)((2+i))/((3+i))|`

Text Solution

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Given that, `|(1+i) ((2+i))/((3+i))|=|((2+i+2i+i^(2)))/((3+i))|=|(2+3i-1)/(3+i)|`
`| ((1+3i))/((3+i))|=|((1+3i)(3+i))/((3+i)(3-i))|`
`|(3+9i-i-3i^(2))/(9-i^(2))|=|(1+8i+3)/(9+1)|=|(6+8i)/(10)|`
`=sqrt(6^(2)/(100)+8^(2)/(100))=sqrt((36+64)/(100))=sqrt((100)/(100))=1`
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