Suppose point A on the complex plane represents the complex number $3+4i$. Which of the following operations involving complex numbers results in a solution represented by point A?

• A. Multiplying $3$ by $4i$
• B. Adding $3i$ and $4$
• C. Multiplying $1+4i$ by $3$
• D. Adding $3$ and $4i$

Answer: (D)

Verified step by step guidance

1. Recall that a complex number is represented as \(a + bi\), where \(a\) is the real part and \(b\) is the imaginary part.
2. Identify the complex number given: \$3 + 4i\(, where \)3\( is the real part and \)4$ is the imaginary part.
3. Examine each operation to see if it results in \$3 + 4i$:
4. 1. Multiplying \$3\( by \)4i\( gives \)3 \times 4i = 12i\(, which is purely imaginary and does not match \)3 + 4i$.
5. 2. Adding \$3i\( and \)4\( gives \)4 + 3i\(, which swaps the real and imaginary parts compared to \)3 + 4i$.
6. 3. Multiplying \((1 + 4i)\) by \$3\( gives \)3 + 12i\(, which has the correct real part but a different imaginary part than \)3 + 4i$.
7. Therefore, the operation that directly results in \$3 + 4i\( is adding \)3\( and \)4i$.