## Wednesday, 30 November 2011

The following is copy/paste from the online textbook. I thought this reading was pretty funny. The (square root) sign doesn't copy and paste, so I had to fill that in. Apparently blogger (Word does the same) thinks THAT is imaginary!

The form a + bi is called the standard form of a complex number. The real number a is called the real part of the complex number, and b is called the imaginary part. (Note that b is a real number even though it is called the imaginary part.) The following list exemplifies this terminology.

* 1. The number 7 + 5i is a complex number that has a real part of 7 and an imaginary part of 5.
* 2. The number 2/3 + i(Square root)2 is a complex number that has a real part of and an imaginary part of . (It is easy to mistake (square root) 2i for (square root) 2i . Thus it is customary to write i(square root) 2 instead of (square root) 2i to avoid any difficulties with the radical sign.)
* 3. The number −4 − 3i can be written in the standard form −4 + (−3i) and therefore is a complex number that has a real part of −4 and an imaginary part of −3. (The form −4 − 3i is often used, but we know that it means −4 + (−3i).)
* 4. The number −9i can be written as 0 + (−9i); thus it is a complex number that has a real part of 0 and an imaginary part of −9. (Complex numbers, such as −9i, for which a = 0 and b fi 0 are called pure imaginary numbers.)
* 5. The real number 4 can be written as 4 + 0i and is thus a complex number that has a real part of 4 and an imaginary part of 0.

Wil said...

Ugh. One thing I hated about math in school (I otherwise loved math) was that the word "imaginary" was used to describe certain types of numbers.

In a sense, all numbers are imaginary, in that they're purely mental -- intangible (by actual definitions of those words).

If you have two apples, you don't have a "two". The two part is something that only happened in your mind. All you have in real life are apples.

So when mathematicians take words that already have specific meanings and then attempt to make up new meanings of those words, they've lost me...

MamaOlive said...

I just loved the part where we call 5 the imaginary part, even though it's real. And it's easy to mistake 5i for 5i. Um, because they're identical?

Thanks for commenting.