Question

What are the steps to simplify (5+3i)−(2+7i)? Match each step with the correct expression.

A) 3+4i
B) 3−4i
C) 7+10i
D) 7−10i

Answer 1

To simplify the expression (5+3i)−(2+7i), you subtract the real numbers and imaginary numbers separately, getting 3 for the real part and −4i for the imaginary part, leading to the answer 3−4i.

Step-by-step explanation:

To simplify the expression (5+3i)−(2+7i), we need to subtract the real parts and the imaginary parts separately:

1. Subtract the real parts: 5 − 2 which equals 3.
2. Subtract the imaginary parts: 3i − 7i which equals −4i.
3. Combine the real and imaginary results to get the simplified expression 3 − 4i.

It is important to eliminate terms wherever possible to simplify the algebra. Using this approach, we check that the simplified solution is reasonable and reflects the subtraction of each part of the complex numbers.

The correct answer is B) 3−4i.