Cauchy-Riemann Equations: Definition & Examples


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The complex function f(z) is given by x2 - y2 + i 2xy. The real part is u(x,y). What is the partial derivative of u with respect to x?

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1. One of the Cauchy-Riemann equations compares ux to _____.

2. If the Cauchy-Riemann equations are true, then the derivative of f(z) is _____.

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About This Quiz & Worksheet

For this interactive quiz and worksheet combo, you are asked about the concept of Cauchy-Riemann equations. Questions will focus on partial derivatives as well as the existence of a derivative in a given equation.

Quiz & Worksheet Goals

You will see the following topics in the questions of the quiz:

  • Finding a partial derivative
  • Derivatives of a function when Cauchy-Riemann equations are true
  • The existence of a function's derivative
  • Making comparisons in Cauchy-Riemann equations

Skills Practiced

  • Information recall - remember what you have learned about partial derivatives
  • Problem solving - use what you know to solve practice problems and find partial derivatives
  • Knowledge application - use your skills to answer questions about the existence of derivatives

Additional Learning

To practice with more equations, visit the lesson titled Cauchy-Riemann Equations: Definition & Examples. Inside, you can look at the following extra material:

  • Complex functions
  • Derivatives of complex functions
  • Applying Cauchy-Riemann equations