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

Thread starter metgt4
Start date Jan 14, 2010
Tags

Analysis Complex Complex analysis

In summary, an Argand Diagram is a graphical representation of complex numbers with a horizontal axis for the real part and a vertical axis for the imaginary part. Plotting ln(3+4i) on an Argand Diagram allows one to visualize the complex logarithm and better understand its properties. To plot ln(3+4i), the number must be converted into polar form and then plotted according to its polar coordinates. The position of ln(3+4i) on the Argand Diagram indicates its real and imaginary parts. The Argand Diagram of ln(3+4i) can provide insight into the behavior of complex logarithms and the relationship between their real and imaginary parts.

Jan 14, 2010

metgt4

Homework Statement

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

The Attempt at a Solution

ln(3+4i)
= ln(3e^2(pi)n + 4e^{i[(pi)/2 + 2(pi)n]}
= i2(pi)n + ln(3+4e^i(pi)/2
= ?

Where do I go next with this?

Thanks!
Andrew

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Jan 14, 2010

payumooli

ln z = ln |z| + i arg(z)

z = x + iy

What is an Argand Diagram?

An Argand Diagram is a graphical representation of complex numbers. It consists of a horizontal axis representing the real part of the number and a vertical axis representing the imaginary part.

What is the purpose of plotting ln(3+4i) on an Argand Diagram?

The purpose of plotting ln(3+4i) on an Argand Diagram is to visualize the complex logarithm of the given number. This can help in understanding the properties and behavior of complex logarithms.

How do you plot ln(3+4i) on an Argand Diagram?

To plot ln(3+4i) on an Argand Diagram, first convert the number into polar form. Then, plot the point corresponding to the polar coordinates (ln(r),θ) on the Argand Diagram, where r is the modulus or distance from the origin and θ is the argument or angle from the positive real axis.

What does the position of ln(3+4i) on the Argand Diagram indicate?

The position of ln(3+4i) on the Argand Diagram indicates the value of the complex logarithm in terms of its real and imaginary parts. The horizontal position represents the real part and the vertical position represents the imaginary part.

What can be inferred from the Argand Diagram of ln(3+4i)?

The Argand Diagram of ln(3+4i) can help in understanding the behavior of complex logarithms. It can show the periodic nature of complex logarithms and the relationship between the real and imaginary parts of the number.