The correct option is C 8i (a+ib)^2= 15+8i nbsp; nbsp; nbsp; nbsp; ; nbsp; nbsp; nbsp; nbsp; nbsp; (x+iy)^2= 15 8i a^2 ...

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Particular Solution of a Differential Equation

√-15+8i-√-15-...

Question

$\sqrt{- 15 + 8 i} - \sqrt{- 15 - 8 i} =$

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Solution

The correct option is C 8i
$(a + i b)^{2} = - 15 + 8 i$ ; $(x + i y)^{2} = - 15 - 8 i$
$a^{2} - b^{2} = - 15$ $x^{2} - y^{2} - 15$
$2 a b = 8$ $2 x y = - 8$
$a^{2} + b^{2} = 17$ $x^{2} + y^{2} = 17$
$∴$ solving equations obtained
$\sqrt{- 15 + 8 i} = \pm (1 + 4 i)$ ; $\sqrt{- 15 - 8 i} = \pm (1 - 4 i)$
$∴ \sqrt{- 15 + 8 i} - \sqrt{- 15 - 8 i} = {\pm 8 i, \pm 2}$

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