If complex numbers (x -2y) + i(3x -y) and (2x -y) + i(x -y + 6) are conjugates of each other, then |

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4-1.Complex numbers

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If complex numbers $(x -2y) + i(3x -y)$ and $(2x -y) + i(x -y + 6)$ are conjugates of each other, then $|x + iy|$ is $(x,y \in R)$

A

$1$

B

$\sqrt2$

C

$2$

D

$4$

Solution

$(x-2 y)+i(3 x-y)=(2 x-y)-i(x-y+6)$

comparing real and imaginary parts

$x+y=0 $ and $2 x-y+3=0$

$\Rightarrow x=-1, y=1$

$|x+i y|=\sqrt{2}$

Standard 11

Mathematics

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