What is a if (2-i)(a-bi) = 2+9i ?

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.