Complex Numbers II

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!