# Answer to Question #18848 in Calculus for Bob

Question #18848

Find the real numbers a and b such that the equation is true.

(a+6) + 2bi=6-5i

(a+6) + 2bi=6-5i

Expert's answer

a + 6 + 2bi = 6 - 5i

(6 + 5i) (a + 6 + 2bi) = (6 + 5i) (6 - 5i) = 36 - 25i^2 = 61

6a + 36 + 12bi + 5ai + 30i + 10bi^2 = 61

6a + i (5a + 12b + 30) - 10b = 25

5a + 12b = -30

6a - 10b = 25

25a + 60b = -150

36a - 60b = 150

61a = 0; a = 0; b = -2.5

(6 + 5i) (a + 6 + 2bi) = (6 + 5i) (6 - 5i) = 36 - 25i^2 = 61

6a + 36 + 12bi + 5ai + 30i + 10bi^2 = 61

6a + i (5a + 12b + 30) - 10b = 25

5a + 12b = -30

6a - 10b = 25

25a + 60b = -150

36a - 60b = 150

61a = 0; a = 0; b = -2.5

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