Answer:
a = 3 and b = 1
Step-by-step explanation:
multiply both sides by 2 + i , to eliminate the fraction
1 + ai = (2 + i)(1 + bi) = 2 + 2bi + i + bi² ( i² = - 1 ), hence
1 + ai = 2 + (2b + 1)i - b = 2 - b + i(2b + 1)
equating coefficients of like terms
equating real part
2 - b = 1 ⇒ - b = 1 - 2 = - 1 ⇒ b = 1
equating imaginary part
a = 2b + 1 = 2 + 1 = 3
