Prove that he expression -1 - m -i -1 - m-1 - m - i-1 - m - -1 - m - i -1 - m-1 - m -i -1 - m m - R simplifies to 2m-

Rationalise numerator and denominator in both the terms of expression. #160;on rationalisation we get. #160; (√( (1+m) ) +i√( (1 m) ) ) ^ 2 / 2 (√( ( ...

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Standard XII

Mathematics

Rationalization Method to Remove Indeterminate Form

Prove that he...

Question

Prove that he expression $\frac{\sqrt{(1 + m)} + i \sqrt{(1 - m)}}{\sqrt{(1 + m)} - i \sqrt{(1 - m)}} - \frac{\sqrt{(1 - m)} + i \sqrt{(1 + m)}}{\sqrt{(1 - m)} - i \sqrt{(1 + m)}} (m \in R)$ simplifies to 2m.

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Solution

rationalise numerator and denominator in both the terms of expression.
on rationalisation we get.
$\frac{{(\sqrt{(1 + m)} + i \sqrt{(1 - m)})}^{2}}{2} - \frac{{(\sqrt{(1 - m)} + i \sqrt{(1 + m)})}^{2}}{2}$
$= \frac{(1 + m - 1 + m + 2 * i \sqrt{(1 + m) (1 - m)}) - (1 - m - 1 - m + 2 * i \sqrt{(1 + m) (1 - m)})}{2}$
=2m

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Prove that he expression √(1+m)+i√(1−m)√(1+m)−i√(1−m)−√(1−m)+i√(1+m)√(1−m)−i√(1+m)(m∈R) simplifies to 2m.

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Prove that he expression $\frac{\sqrt{(1 + m)} + i \sqrt{(1 - m)}}{\sqrt{(1 + m)} - i \sqrt{(1 - m)}} - \frac{\sqrt{(1 - m)} + i \sqrt{(1 + m)}}{\sqrt{(1 - m)} - i \sqrt{(1 + m)}} (m \in R)$ simplifies to 2m.