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UPSC NDA Math Model Paper 7

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Question : 8 of 120

Marks: +1, -0

If

x+iy=\begin{vmatrix} 6i & -3i & 1 \\ 4 & 3i & -1 \\ 20 & 3 & i \end{vmatrix}

x

- iy equal to?

3 + i
1 + 3i
3i
0

Solution:

Given,

x+iy=\begin{vmatrix} 6i & -3i & 1 \\ 4 & 3i & -1 \\ 20 & 3 & i \end{vmatrix}

\Rightarrow x+iy=6i(3i^{2}+3)+3i(4i+20)

+1(12-60i)

\Rightarrow x+iy=6i(3i^{2}+3)+12i^{2}

+60i+12-60i

We know that

i^{2}=-1

\Rightarrow x+iy=6i[3(-1)+3]+12(-1)

+60i+12-60i

\Rightarrow x+iy=0

\Rightarrow x+iy=0+i0

\Rightarrow x=0

and

y=0

Consider,

x

- iy Put the value of

x

and

y

in above expression, we get

\Rightarrow x-iy=0-i0

\Rightarrow x-iy=0

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