Question

If


`(1 + ai)/(2 + i) = 1 + bi`
where a and b are constant terms, fibd the values of a and b.

Answer 1

a = 3 and b = 1

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