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Question
Find `|(1 + i) ((2 + i))/((3 + i))|`.
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Solution
`|(1 + i) ((2 + i))/((3 + i)) xx (3 - i)/(3 - i)|`
= `|(1 + i) . (6 - 2i + 3i - i^2)/(9 - i^2)|`
= `|((1 + i).(7 + i))/(9 + 1)|`
= `|(7 + i + 7i + i^2)/10|`
= `|(7 + 8i - 1)/10|`
= `|(6 + 8i)/10|`
= `|3/5 + 4/5 i|`
= `sqrt((3/5)^2 + (4/5)^2)`
= 1
Hence, `|(1 + i) ((2 + i)/(3 + i))|` = 1.
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