Textbook Question
In Exercises 21–28, divide and express the result in standard form.
2+3i / 2+i
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0. Review of College Algebra
Complex Numbers
Multiple Choice
Suppose point A on the complex plane represents the complex number . Which of the following operations involving complex numbers results in a solution represented by point A?
A
Multiplying by
B
Adding and
C
Multiplying by
D
Adding and
Verified step by step guidance1
Recall that a complex number is represented as \(a + bi\), where \(a\) is the real part and \(b\) is the imaginary part.
Identify the complex number given: \(3 + 4i\), where \(3\) is the real part and \(4\) is the imaginary part.
Examine each operation to see if it results in \(3 + 4i\):
1. Multiplying \(3\) by \$4i$ gives \(3 \times 4i = 12i\), which is purely imaginary and does not match \(3 + 4i\).
2. Adding \$3i$ and \(4\) gives \(4 + 3i\), which swaps the real and imaginary parts compared to \(3 + 4i\).
3. Multiplying \((1 + 4i)\) by \(3\) gives \(3 + 12i\), which has the correct real part but a different imaginary part than \(3 + 4i\).
Therefore, the operation that directly results in \(3 + 4i\) is adding \(3\) and \$4i$.
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