Solve -4ab - 2 a2 - b2i

The correct option is B #160; √(2)( a b ) #10; #10;Consider the equation , √(4ab 2(a^2+b^2)).i #10; #10; #10; #10; #160; #10;√ ...

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Byju's Answer

Standard XII

Mathematics

Integration by Substitution

Solve √4ab ...

Question

Solve $\sqrt{4 a b - 2 (a^{2} - b^{2}) i}$

\pm {\frac{(a - b) + i (a + 2 b)}{2}}

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\pm {(i + 5 b) + i (a - 4 b)}

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- \sqrt{2} (a - b)

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\mp {(i + b) + i (a - b)}

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Solution

The correct option is B $- \sqrt{2} (a - b)$

Consider the equation , $\sqrt{4 a b - 2 (a^{2} + b^{2})} . i$

$\sqrt{4 a b - 2 (a^{2} + b^{2})} . i = \sqrt{4 a b i - 2 (a^{2} + b^{2})} . i$

$= \sqrt{(4 a b - 2 a^{2} - 2 b^{2})} . i$

$= \sqrt{- 2 (2 a b - a^{2} - b^{2})} . i$

$= \sqrt{- 2 {(a - b)}^{2}} . i$

$= \sqrt{2} (a - b) i \sqrt{- 1}$

$∵ \sqrt{- 1} = i$

$= \sqrt{2} (a - b) i . i$

$= \sqrt{2} (a - b) i^{2}$

$= \sqrt{2} (a - b) (- 1)$

$= - \sqrt{2} (a - b)$

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Solve √4ab−2(a2−b2)i

The correct option is B −√2(a−b) Consider the equation ,√4ab−2(a2+b2).i √4ab−2(a2+b2).i=√4abi−2(a2+b2).i =√(4ab−2a2−2b2).i =√−2(2ab−a2−b2).i =√−2(a−b)2.i =√2(a−b)i√−1 ∵√−1=i =√2(a−b)i.i =√2(a−b)i2 =√2(a−b)(−1) =−√2(a−b)

Solve $\sqrt{4 a b - 2 (a^{2} - b^{2}) i}$