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Topic: [ap-calculus] Number System
Replies: 1   Last Post: Oct 17, 2012 4:34 PM

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Alan Lipp

Posts: 1,091
Registered: 12/6/04
RE: [ap-calculus] Number System
Posted: Oct 17, 2012 4:34 PM
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Debbie,

I am not sure what you mean in (1) by "Number System" since there are infinitely many different "systems." But I don't think either categorization is correct since I have never heard the term Imaginary used as you use it in (1). The term in common use is "pure imaginary" which is a subset of the complex numbers.

As for (2) the set of complex numbers are isomorphic to the Cartesian plane as every complex number can be written as a + bi and identified with the pair of real numbers (a,b). The real numbers can be written as a + 0i and identified with the subset of points (a, 0) in the plane. In other words, the real numbers are the real line, the x-axis, and form a a subset of the complex numbers.

Similarly, the numbers bi = 0 + bi are often called "pure imaginary" numbers to indicate that their real part is zero. They can be identified with the imaginary axis of points (0, b). In this sense the set of real numbers and the set of pure imaginary numbers are each subsets of the complex plane, but they do not exhaust the complex numbers. That is, their union is not all of C.

Alan

Alan Lipp
Williston Northampton School


-----Original Message-----
From: Debbie Bricker [mailto:dbricker@cathedralcatholic.org]
Sent: Wednesday, October 17, 2012 1:25 PM
To: AP Calculus
Subject: [ap-calculus] Number System

NOTE:
This ap-calculus EDG will be closing in the next few weeks. Please sign up for the new AP Calculus Teacher Community Forum at https://apcommunity.collegeboard.org/getting-started
and post messages there.
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We are having this discussion among our department....which is correct?
1) Number System having two subsets: Real(rational and irrational) and Imaginary(which includes complex numbers) OR

2) Complex Number System having two subsets: Real and Imaginary
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