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 the real parts: \(2 - 4\).
4. Combine the imaginary parts: \(8i + i\).
5. Express the result in standard form \(a + bi\), where \(a\) is the real part and \(b\) is the imaginary part.