Math Problem Statement

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

Solution

The graph above shows the complex number z=1+iz = 1 + i (in blue) and its complex conjugate z=1i\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.

Would you like any further explanation or additional details?

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!

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Polar Coordinates
Complex Conjugates

Formulas

r = |z| = sqrt(x^2 + y^2)
theta = arg(z) = arctan(y/x)
Complex Conjugate: z = x - iy

Theorems

Modulus and Argument of a Complex Number
Geometric Reflection of Complex Conjugates

Suitable Grade Level

Grades 10-12