Knowing (2 - i)*(a - bi) = 2 + 9i, where i is the imaginary unit and a and b are real numbers, what is a?

You need to open the brackets such
that:

`2a - 2bi - ai + bi^2 = 2 +
9i`

You need to substitute -1 for  class="AM">`i^2` (complex number theory) such
that:

`2a - 2bi - ai - b = 2 +
9i`

You need to factor out i such
that:

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

Equating the coefficients of like parts
yields:

`2a - b = 2 =gt b = 2a -
2`

`-a - 2b = 9
`

You need to substitute class="AM">`2a - 2`  for b in equation `-a - 2b =
9`  such that:

`-a -
2(2a - 2) = 9`

`-a - 4a
+ 4 = 9 =gt -5a = 9 - 4 =gt -5a = 5 =gt a =
-1`

Hence, evaluating the value
of a yields `a = -1`
.