Plotting ln(3+4i) on an Argand Diagram - Andrew's Query

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SUMMARY

The discussion centers on plotting the complex logarithm ln(3+4i) on an Argand diagram. The user, Andrew, attempts to express ln(3+4i) using the formula ln z = ln |z| + i arg(z), leading to the equation ln(3+4i) = ln(5) + i(0.9273 + 2πn). The key challenge is determining the argument of the complex number and how to represent it graphically on the Argand diagram. The solution requires understanding both the magnitude and the angle of the complex number.

PREREQUISITES
  • Complex number representation in the form z = x + iy
  • Understanding of the logarithmic function for complex numbers
  • Familiarity with Argand diagrams
  • Knowledge of polar coordinates and their relation to complex numbers
NEXT STEPS
  • Study the properties of complex logarithms, specifically ln(z) = ln|z| + i arg(z)
  • Learn how to calculate the magnitude and argument of complex numbers
  • Explore graphical representation of complex numbers on Argand diagrams
  • Investigate the periodic nature of complex logarithms and the implications of adding 2πn
USEFUL FOR

Students studying complex analysis, mathematics educators, and anyone interested in visualizing complex functions on Argand diagrams.

metgt4
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Homework Statement



On an Argand diagram, plot ln(3+4i)


The Attempt at a Solution



ln(3+4i)
= ln(3e2(pi)n + 4ei[(pi)/2 + 2(pi)n]
= i2(pi)n + ln(3+4ei(pi)/2
= ?

Where do I go next with this?

Thanks!
Andrew
 
Physics news on Phys.org
ln z = ln |z| + i arg(z)

z = x + iy
 

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