Final answer:
The real number solutions for the equation (8+6i)+(44-17i)-(a-bi)=0 are a = 52 and b = -11, which are obtained by equating both the real and imaginary parts of the equation to zero and solving for a and b.
Step-by-step explanation:
We are asked to find the real numbers a and b if the equation (8+6i)+(44-17i)-(a-bi)=0 is given, where i is the imaginary unit.
Starting with the given equation, we combine like terms:
8 + 44 - a + (6i + 17i + bi) = 0
Summing the real parts and the imaginary parts separately, we get:
52 - a + (6i - 17i - bi) = 0
Next, we split this into real and imaginary parts. In order to satisfy this equation, the real part must equate to zero and the imaginary part must also equate to zero.
For the real part: 52 - a = 0
For the imaginary part: 6i - 17i - bi = 0
Solving for a from the real part: a = 52
Solving for b from the imaginary part: -11i - bi = 0, which gives us b = -11
Therefore, a = 52 and b = -11 are the solutions to the equation.