Question

Find real numbers a and b such that the equation is true. (a + 1) + (b - 2)i = 4 + 6i

A) a = 3, b = 8
B) a = 5, b = 4
C) a = 2, b = 6
D) a = 6, b = 1

Answer 1

To solve the equation, we equate the real and imaginary parts of the left-hand side and right-hand side separately to find the values of a and b. The correct answer is A) a = 3, b = 8.

Step-by-step explanation:

Given (a + 1) + (b - 2)i = 4 + 6i, we can equate the real and imaginary parts of the left-hand side and right-hand side of the equation separately.

Equating the real parts, we get a + 1 = 4, which gives a = 3.

Equating the imaginary parts, we get b - 2 = 6, which gives b = 8.

Therefore, the correct answer is A) a = 3, b = 8.