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.