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Question
If z is a non-zero complex number, then \[\left| \frac{\left| z \right|^2}{zz} \right|\] is equal to
Options
`|overlinez/z|`
\[\left| z \right|\]
`|overlinez|`
none of these
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Solution
`|overlinez/z|`
`||overlinez|^2/(zoverlinez)| = ||overlinez|^2/|z|^2| (becausez overlinez= |z|^2)`
Let `z = a - ib`
⇒ `|z| = sqrt(a^2 +b^2)`
Let `overlinez = a - ib`
⇒ `|overlinez| = sqrt(a^2 +b^2)`
`therefore ||overlinez|^2/(zoverlinez)| = ||overlinez|^2/|z|^2|`
= `|overlinez/z|`
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