Find the difference. Express your answer in standard form. $\(\left\)(2+8i\(\right\))-\(\left\)(4-i\(\right\))$

• A. $-2+9i$
• B. $6+7i$
• C. $2+7i$
• D. $2-9i$

Answer: (A)

Verified step by step guidance

1. Identify the expression to simplify: (2 + 8i) - (4 - i).
2. Distribute the negative sign across the second complex number: (2 + 8i) - 4 + i.
3. Combine like terms by adding the real parts and the imaginary parts separately: (2 - 4) + (8i + i).
4. Simplify the real part: 2 - 4 = -2.
5. Simplify the imaginary part: 8i + i = 9i. Therefore, the expression simplifies to -2 + 9i.