-8-6 i-A- 1 - 3 iB- -1-3 iC- -1-3 iD- -3-i

The correct option is B Given that √( 8 6i)=x+iy=z ⇒ 8 6i=(x+iy)^2 ∴ nbsp;x^2+y^2 = 8 ......(i) And 2xy= 6 ........(ii) nbsp; Now x^2+y^2 = √(64+36)=±10 ...

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Standard XI

Mathematics

Square Root of a Complex Number

√-8-6 i=A. 1 ...

Question

$\sqrt{- 8 - 6 i}$ =

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Solution

The correct option is B

Given that $\sqrt{- 8 - 6 i}$ =x+iy=z

$\Rightarrow$ -8-6i= $(x + i y)^{2}$

$∴$ $x^{2}$ + $y^{2}$ =-8 ......(i) And 2xy=-6 ........(ii)

Now $x^{2}$ + $y^{2}$ = $\sqrt{64 + 36}$ = $\pm$ 10 ........(iii)

From (i) and (ii),we get x= $\pm$ 1 and y= $\pm$ 3

Hence z= $\pm$ (1-3i)

Trick: Since{ $\pm$ $(1 - 3 i)^{2}$ } = -8-6i

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√−8−6i=

The correct option is B Given that √−8−6i=x+iy=z ⇒ -8-6i=(x+iy)2 ∴ x2+y2 =-8 ......(i) And 2xy=-6 ........(ii) Now x2+y2 = √64+36=±10 ........(iii) From (i) and (ii),we get x=±1 and y=±3 Hence z=±(1-3i) Trick: Since{±(1−3i)2} = -8-6i

$\sqrt{- 8 - 6 i}$ =