Polar Coordinates Homework: Understanding Second Equation

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SUMMARY

The discussion focuses on deriving the second equation in polar coordinates from a complex notation perspective. The user attempted to express the derivative of a complex variable, z_dot, as a function of polar coordinates using the expression z = r * exp(iθ). The solution involves differentiating z and equating real and imaginary parts after converting from complex to polar notation. The key steps include using the product rule and recognizing the relationship between the derivatives of r and θ.

PREREQUISITES
  • Understanding of polar coordinates and their representation in complex analysis.
  • Familiarity with differentiation in complex functions.
  • Knowledge of the product rule in calculus.
  • Basic concepts of real and imaginary parts of complex numbers.
NEXT STEPS
  • Study the differentiation of complex functions in polar coordinates.
  • Learn about the product rule and its application in complex analysis.
  • Explore the relationship between polar and rectangular coordinates in complex numbers.
  • Review examples of equating real and imaginary parts in complex equations.
USEFUL FOR

Students studying complex analysis, particularly those tackling polar coordinates and their applications in calculus. This discussion is beneficial for anyone looking to deepen their understanding of complex derivatives and their transformations.

rsaad
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Homework Statement



In the attachment, I do not understand how we got the second equation in terms of polar coordinates.




Homework Equations





The Attempt at a Solution




I tried doing it by writing z_dot = (...)z and then plugging in r* exp i theta, but to no avail.
 

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rsaad said:

Homework Statement



In the attachment, I do not understand how we got the second equation in terms of polar coordinates.

Homework Equations


The Attempt at a Solution

I tried doing it by writing z_dot = (...)z and then plugging in r* exp i theta, but to no avail.

Show how you tried it. z'=r'e^(iθ)+iθ're^(iθ). Try going straight from the "complex notation" to the "polar notation". Divide both sides by e^(iθ) and equate real and imaginary parts.
 

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