Class notes
lecture notes
- Course
- Pre Calculus and Calculus
- Institution
- Walter Sisulu University (WSU)
Notes on conjugates and modulus
[Show more]
Seller
Follow
Content preview
Conjugate And ModulusIn the previous section we looked at algebraic operations on complex numbers.Th
other operations that we should take a look at since they tend to show up on occa
a look at quite a few nice facts about these operations.
Complex Conjugate
The first one we’ll look at is the complex conjugate, (or just the conjugate).Given
number z = a + bi the complex conjugate is denoted by ¯z̄¯ and is defined to be,
¯z̄
¯ = a − bi
In other words, we just switch the sign on the imaginary part of the number.
Here are some basic facts about conjugates.
¯¯¯
¯z̄
¯ =z
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
z1 ± z2 = ¯z̄¯ 1 ± ¯z̄¯ 2
¯z¯¯¯¯¯z
1 2
¯¯¯ = ¯z̄¯ 1 ¯z̄¯ 2
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯z̄
¯
z1
( )=
1
z2 ¯z̄
¯
2
The first one just says that if we conjugate twice we get back to what we started w
hopefully this makes some sense.The remaining three just say we can break up s
products and quotients into the individual pieces and then conjugate.
So, just so we can say that we worked a number example or two let’s do a couple
illustrating the above facts.
Example 1 Compute each of the following.
¯¯¯
(a) ¯z̄¯ for z = 3 − 15i
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
(b) z1 − z2 for z1 = 5 + i and z2 = −8 + 3i
(c) ¯z¯¯¯1¯ − ¯z¯¯¯2¯ for z1 = 5 + i and z2 = −8 + 3i
Hide Solution !
There really isn’t much to do with these other than to so the work so,
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 EFT, 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 this summary 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 this summary for R100,00. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
73216 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now