Question

21. Let a and b be real numbers. If

(a+bi)-(3-5i) = 7-4i,
what are the values of a and b?
A. a-10, b=-9
B. a 10, b=1
C. a=4, b=-9
D. a=4, b=1

Answer 1

A. a = 10, b = -9

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.