find the value of r & thita and plot the graph of complex conjugate of complex number 1+i

The graph above shows the complex number \( z = 1 + i \) (in blue) and its complex conjugate \( \overline{z} = 1 - i \) (in red) on the complex plane. The real parts are plotted along the x-axis, and the imaginary parts along the y-axis.

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Here are 5 related questions:
1. How do you find the polar form of a complex number for general cases?
2. What is the geometric interpretation of the modulus and argument of a complex number?
3. How does the graph of a complex conjugate relate to the original complex number geometrically?
4. How do you convert from polar form back to rectangular form?
5. What happens to the argument when you take the complex conjugate?

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

Find the value of r & theta and plot the graph of the complex conjugate of the complex number 1+i.

Learn how to calculate the polar form (r and theta) of the complex number 1+i and how to plot its complex conjugate. This solution explains the key concepts of modulus, argument, and geometric reflection in the complex plane. Suitable for students in Grades 10-12.

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