Class notes
lecture notes
- Course
- Institution
notes on complex planes
[Show more]
Seller
Follow
LUE
Content preview
Polar & Exponential FormMost people are familiar with complex numbers in the form z = a + bi, howeve
alternate forms that are useful at times. In this section we’ll look at both of those
couple of nice facts that arise from them.
Geometric Interpretation
Before we get into the alternate forms we should first take a very brief look at a
interpretation of complex numbers since this will lead us into our first alternate f
Consider the complex number z = a + bi. We can think of this complex numbe
point (a, b) in the standard Cartesian coordinate system or as the vector that st
and ends at the point (a, b). An example of this is shown in the figure below.
In this interpretation we call the x-axis the real axis and the y-axis the imagina
call the xy-plane in this interpretation the complex plane.
Note as well that we can now get a geometric interpretation of the modulus. Fr
above, we can see that |z| = √a2 + b2 is nothing more than the length of the
using to represent the complex number z = a + bi. This interpretation also tell
inequality |z1 | < |z2 | means that z1 is closer to the origin (in the complex plane
Polar Form
Let’s now take a look at the first alternate form for a complex number. If we thin
complex number z = a + bi as the point (a, b) in the xy-plane we also know t
represent this point by the polar coordinates (r, θ), where r is the distance of th
origin and θ is the angle, in radians, from the positive x-axis to the ray connecti
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller LUE. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $5.69. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
73918 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now