- #1
snshusat161 said:And if z = x + iy
then in polar form it will be written as
z = r (cos[tex]\theta[/tex] + i sin[tex]\theta[/tex]
where r = [tex]\sqrt{x^2 + y^2}[/tex] and [tex]\theta[/tex] = arg(z)
saying LaTeX Code: \\theta=arg(z) is trivial since if you know what one means then you should know what the other means
An Argand diagram is a mathematical representation of complex numbers using a two-dimensional coordinate system. It was named after mathematician Jean-Robert Argand and is commonly used to visualize complex numbers and their properties.
To draw an Argand diagram, you first need to plot the real part of the complex number on the horizontal axis and the imaginary part on the vertical axis. The point where these two values intersect represents the complex number. You can also use different colors or shapes to represent different complex numbers on the diagram.
An Argand diagram is used to visualize complex numbers and their relationships, such as addition, subtraction, multiplication, and division. It can also help in understanding the geometric interpretation of complex numbers, such as their modulus and argument.
Yes, an Argand diagram can be used to solve equations involving complex numbers. By plotting the given complex numbers on the diagram, you can easily determine the solutions to equations such as z = a + bi or z^2 = a + bi.
While an Argand diagram is a useful tool for understanding complex numbers, it does have its limitations. It can only represent complex numbers in two dimensions and may not be able to accurately show the magnitude and direction of very large or very small complex numbers. Also, the diagram cannot be used to represent complex functions or equations with more than two variables.