A complex number, (a + bi), multiplied by (2 + 3i) and added to - i gives the product of (-11 + 5i) and (1-i)

a = ? b=?

Working backwards (-11 + 5i) (1 - i) = - 11 + 11i + 5i + 5 = - 6 + 16i

subtracting - i we have - 6 + 16i - (-i) = - 6 + 17i

(a + bi) (2 + 3i) = 2a + 3ai + 2bi + 3bi^2 = 2a - 3b + (3a + 2b) i

2a - 3b + (3a + 2b) i = - 6 + 17i

EQuating real and imaginary parts:-

2a - 3b = - 6

3a + 2b = 17

solving this for a and b gives a = 3 and b = 4