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The task involves matching the complex numbers (given on the right) with their corresponding arguments (angles) in radians (given on the left). The arguments are standard angles in the complex plane, and the complex numbers are expressed in rectangular form \(a + bj\), where \(j\) represents the imaginary unit.

### To solve this, let's break it down step by step:

1. **\( \pi/4 \) (45 degrees):**
   - This is the angle where both real and imaginary parts are equal. The complex number matching this angle is \( 7 + 7j \).

2. **\( \pi/6 \) (30 degrees):**
   - At this angle, the real part is larger than the imaginary part. The correct complex number is \( \frac{7}{\sqrt{3}} + \frac{7}{3}j \).

3. **\( \pi/3 \) (60 degrees):**
   - The imaginary part is larger than the real part. The corresponding complex number is \( \frac{7}{3} + \frac{7}{\sqrt{3}} j \).

4. **\( \pi/2 \) (90 degrees):**
   - Purely imaginary since the real part is zero. The corresponding complex number is \( 7j \).

5. **\( 5\pi/3 \) (300 degrees or -60 degrees):**
   - This angle is in the fourth quadrant, where the real part is positive, and the imaginary part is negative. The correct complex number is \( \frac{7}{3} - \frac{7}{\sqrt{3}} j \).

6. **\( 0 \) (0 degrees):**
   - Purely real with no imaginary part. The corresponding complex number is \( 7 \).

7. **\( 3\pi/2 \) (270 degrees):**
   - Purely imaginary and negative. The corresponding complex number is \( -21 - 7\sqrt{3}j \).

8. **\( \pi \) (180 degrees):**
   - Purely real but negative. The corresponding complex number is \( -7 \).

Now that we've analyzed the correct pairings:

### Correct matches:
- \( \pi/4 \) ↔ \( 7 + 7j \)
- \( \pi/6 \) ↔ \( \frac{7}{\sqrt{3}} + \frac{7}{3}j \)
- \( \pi/3 \) ↔ \( \frac{7}{3} + \frac{7}{\sqrt{3}} j \)
- \( \pi/2 \) ↔ \( 7j \)
- \( 5\pi/3 \) ↔ \( \frac{7}{3} - \frac{7}{\sqrt{3}} j \)
- \( 0 \) ↔ \( 7 \)
- \( 3\pi/2 \) ↔ \( -21 - 7\sqrt{3}j \)
- \( \pi \) ↔ \( -7 \)

Let me know if you'd like more details on any of these!

### Related questions:
1. What is the significance of the argument of a complex number?
2. How do you convert a complex number from rectangular form to polar form?
3. Can you explain how to determine the quadrant of a complex number based on its argument?
4. What is the geometric interpretation of complex numbers on the Argand plane?
5. How does the magnitude of a complex number affect its representation?

**Tip:** When dealing with complex numbers, always check the sign of the real and imaginary components to correctly determine their position on the complex plane.

Ordnen Sie jeder komplexen Zahl ihr Argument zu!

Learn how to match complex numbers to their arguments in radians. This problem involves identifying angles in the complex plane and pairing them with rectangular form complex numbers. Suitable for high school students in Grades 11-12 studying complex numbers and their geometric representations.

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