Answer:
A. a = 10, b = -9
Step-by-step explanation:
Pre-Solving
We are given:
(a+bi)-(3-5i) = 7-4i
We know that a and b are both real numbers, and we want to find what a and b are.
Solving
For imaginary numbers, a is the real part, and bi is the imaginary part. This means that we consider the real numbers like terms, and the imaginary numbers like terms.
So to start, we can open the equation to become:
a + bi - 3 + 5i = 7 - 4i
Based on what we mentioned above:
a - 3 = 7
+ 3 +3
_____________
a = 10
And:
bi + 5i = -4i
-5i -5i
____________j
bi = -9i
Divide both sides by i.
bi = -9i
÷i ÷i
_________
b = -9
So, a = 10, b= -9. The answer is A.
