Class notes
Lecture notes
- Course
- Pre Calculus and Calculus
- Institution
- Walter Sisulu University (WSU)
Short notes on Complex Numbers Arithmetic.
[Show more]
Seller
Follow
Content preview
ArithmeticBefore proceeding in this section let me first say that I’m assuming that you’ve se
complex numbers at some point before and most of what is in this section is goin
you. I am also going to be introducing subtraction and division in a way that you p
seen prior to this point, but the results will be the same and aren’t important for th
sections of this document.
In the previous section we defined addition and multiplication of complex numbe
i2 = −1 is a consequence of how we defined multiplication. However, in practice
multiply complex numbers using the definition. In practice we tend to just multiply
numbers much like they were polynomials and then make use of the fact that we
i2 = −1.
Just so we can say that we’ve worked an example let’s do a quick addition and m
complex numbers.
Example 1 Compute each of the following.
(a) (58 − i) + (2 − 17i)
(b) (6 + 3i) (10 + 8i)
(c) (4 + 2i) (4 − 2i)
Hide Solution #
As noted above, I’m assuming that this is a review for you and so won’t be goin
here.
(a) (58 − i) + (2 − 17i) = 58 − i + 2 − 17i = 60 − 18i
(b) (6 + 3i) (10 + 8i) = 60 + 48i + 30i + 24i2 = 60 + 78i + 24 (−1) =
(c) (4 + 2i) (4 − 2i) = 16 − 8i + 8i − 4i2 = 16 + 4 = 20
It is important to recall that sometimes when adding or multiplying two complex nu
might be a real number as shown in the third part of the previous example!
The third part of the previous example also gives a nice property about complex n
(a + bi) (a − bi) = a2 + b2
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)
72042 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now