If where a and b are constant terms, fibd the values of a and b.

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

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true