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We have to find a given that (2-i)(a-bi) = 2+9i.

Now, (2-i)(a-bi) = 2+9i

=> 2a -ia -2bi + bi^2 = 2+ 9i

=> 2a - ia - 2bi - b = 2+ 9i

=> 2a -b -i ( a+ 2b) = 2+ 9i

Equate the real and imaginary coefficients.

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We have to find a given that (2-i)(a-bi) = 2+9i.

Now, (2-i)(a-bi) = 2+9i

=> 2a -ia -2bi + bi^2 = 2+ 9i

=> 2a - ia - 2bi - b = 2+ 9i

=> 2a -b -i ( a+ 2b) = 2+ 9i

Equate the real and imaginary coefficients.

We get 2a -b = 2 and a + 2b = -9

Now as 2a -b = 2 => b = 2a - 2

substitute this in a + 2b = -9

=> a + 2*( 2a - 2) = -9

=> a + 4a - 4 = -9

=> 5a = -5

=> a = -5/5 = -1

Therefore the required value of a is -1.

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