What Is the Norm and the Argument of a Complex Number?
Since Cartesian form and polar form are equivalent ways to write the same complex number z, there are rules for how to convert between these two forms of representing complex numbers. [1]
Norm
For all complex numbers z = a + bi, you can find the norm r of z as
Argument
For all complex numbers z = a + bi with norm r = √(a2 + b2), you can find the argument 𝜃 using one of the following formulas:
References
[1] “What Is The Norm And The Argument Of A Complex Number?” 2022. House Of Math. https://www.houseofmath.com/encyclopedia/numbers-and-quantities/numbers/complex-numbers/introduction/what-is-the-norm-and-the-argument-of-a-complex-number.
Additional Reading
“Complex Conjugate And Norm”. 2022. books.physics.oregonstate.edu. https://books.physics.oregonstate.edu/LinAlg/conjugate.html.
Videos
This is the introduction to Complex Numbers, and today we’re going to study what is a Complex Number, Complex Conjugate and the Polar Form. As you may or may not know, Complex Numbers are the numbers represented by the following form Z=a+bi, where a and b are real numbers, and i is an “imaginary unit”. Today we also are going to solve the example problem involving Complex Numbers. Stay tuned and check out our video to learn more about complex numbers standard form and simplifying complex numbers!
Everybody loves the complex numbers, and they bring some unique properties to the table that aren’t present in the ordered field of real numbers. However, something is lost as well – and today we’ll discuss exactly what that is as we attempt to order the complex numbers.