Final answer:
The missing variables in the complex number equation (a + 6) + 2bi = 6 - 5i are a = 0 and b = -2.5. It involves equating the real and imaginary parts on both sides of the equation.
Step-by-step explanation:
The equation (a + 6) + 2bi = 6 - 5i represents a complex number equation where the missing variables are the real part 'a' and the imaginary part 'b' of a complex number. To solve for 'a' and 'b', we compare the real and imaginary parts on both sides of the equation. The real parts are (a + 6) on the left and 6 on the right, and the imaginary parts are 2bi on the left and -5i on the right.
Equating the real parts gives us: a + 6 = 6, which simplifies to a = 0. Equating the imaginary parts gives us: 2b = -5, which simplifies to b = -5/2 or b = -2.5. Thus, the missing variables are a = 0 and b = -2.5.
This solution requires understanding that complex numbers are equal if and only if their corresponding real and imaginary parts are equal. This concept is essential in finding the values of a and b here.