Represent the complex number 2 + 3𝑖 and its conjugate on a complex plane.

To represent the complex number \( z = 2 + 3i \) and its conjugate on the complex plane:

1. **Complex Number \( z = 2 + 3i \):**
   - This number has a real part of 2 and an imaginary part of 3.
   - On the complex plane, the x-axis (horizontal) represents the real part, and the y-axis (vertical) represents the imaginary part.
   - So, the point \( (2, 3) \) corresponds to \( z \), where 2 is the real part and 3 is the imaginary part.

2. **Conjugate \( \bar{z} = 2 - 3i \):**
   - The conjugate of \( z \) is obtained by changing the sign of the imaginary part.
   - In this case, \( z = 2 + 3i \) and its conjugate \( \bar{z} = 2 - 3i \) has the same real part but the imaginary part is \(-3\).
   - So, \( \bar{z} \) is represented by the point \( (2, -3) \) on the complex plane.

### Plotting on the Complex Plane:
- Plot the point \( (2, 3) \) for \( z = 2 + 3i \).
- Plot the point \( (2, -3) \) for the conjugate \( \bar{z} = 2 - 3i \).
- The two points will be symmetric about the real axis (x-axis).

Would you like a visual representation of this complex plane?

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Here are some relative questions to further your understanding:

1. What is the magnitude of the complex number \( z = 2 + 3i \)?
2. How would you add two complex numbers like \( z_1 = 2 + 3i \) and \( z_2 = 1 + 4i \)?
3. What is the result of multiplying \( z = 2 + 3i \) by its conjugate?
4. How do you interpret the argument (angle) of a complex number in the complex plane?
5. Can you generalize the rule for finding the conjugate of any complex number?

**Tip:** The conjugate of a complex number reflects it across the real axis on the complex plane.

Represent the complex number 2 + 3i and its conjugate on a complex plane.

Learn how to represent the complex number 2 + 3i and its conjugate on a complex plane. This example covers fundamental concepts of complex numbers, how to plot them, and the reflection across the real axis. Suitable for high school students in Grades 10-12.

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