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

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

Answer: (A)

Verified step by step guidance

1. Identify the complex numbers involved in the subtraction: the first complex number is \(\left(2 + 8i\right)\) and the second complex number is \(\left(4 - i\right)\).
2. Rewrite the expression to subtract the second complex number from the first: \(\left(2 + 8i\right) - \left(4 - i\right)\).
3. Distribute the subtraction sign across the second complex number: \$2 + 8i - 4 + i$.
4. Group the real parts together and the imaginary parts together: \((2 - 4) + (8i + i)\).
5. Simplify each group by performing the arithmetic operations: combine the real numbers and combine the imaginary coefficients to express the result in standard form \(a + bi\).