tag:blogger.com,1999:blog-7245208048685880741.post9134194100791882891..comments2023-05-19T10:32:11.137-04:00Comments on Rational Expressions: Complex Numbers Are Two-Part NumbersMichael Pershanhttp://www.blogger.com/profile/17046644130957574890noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-7245208048685880741.post-11270944262019506592014-02-19T22:28:24.979-05:002014-02-19T22:28:24.979-05:00I'm with you on this one Michael. I think of t...I'm with you on this one Michael. I think of them - along with vectors - as an inherently visual thing. I see direction and length, I see horizontal change and vertical change wrapped up in one number that has two characteristics.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7245208048685880741.post-82659847696820267782014-02-18T20:59:31.284-05:002014-02-18T20:59:31.284-05:00To me, that correction that you have to make for e...To me, that correction that you have to make for equivalent fractions points to their fundamental one dimensionality.<br /><br />Michael Pershanhttps://www.blogger.com/profile/17046644130957574890noreply@blogger.comtag:blogger.com,1999:blog-7245208048685880741.post-40657909127715107082014-02-18T20:39:12.735-05:002014-02-18T20:39:12.735-05:00You could treat both fractions and complex numbers...You could treat both fractions and complex numbers as ordered pairs (i.e. two-part numbers). Fractions with the same value but different representations (e.g. 1/2 and 2/4) are then just different points on a line that goes through the origin.<br /><br />I think I prefer the holistic view that fractions and complex numbers (and real numbers) are just "numbers". It's important to note that one cannot just distribute arithmetic operations over individual parts of a fraction or complex number, but depending on what kind of "number" you have, you may need to do things in a slightly different or novel way. I wouldn't imagine this to be any different from the kind of abstraction needed when one first learns algebra and manipulating algebraic expressions.Haohttps://www.blogger.com/profile/02348974241652264510noreply@blogger.com