It can’t get more imaginary than this.
19/09/2011 § 1 Comment
At first, I was a bit upset when we started learning about complex solutions because it meant that we could really no longer just write a simple “No Solution” as an answer for certain problems. Admittedly, I’m still a bit upset that there’s a bit more math to the work I’ll have to do during certain problems that involve finding the square root of negative numbers. The good part is that the concept of using i isn’t too hard; it simply takes a bit of time for me to find out what i-to-the-power-of-something will equal but usually I get it quickly.
One very good reason to have complex solutions is because the fact that it’s used commonly nowadays is sure sign of the potential of a human’s mental capacity. According to BetterExplained.com, “it is a testament to our mental potential that today’s children are expected to understand ideas that once confounded ancient mathematicians.” Also, although complex numbers are theoretical numbers that humans invent, they are useful and they fill in the blanks of numbers and ideas we don’t know how to explain completely. A little like negatives, there was a concept that was confusing and mathematicians in the past invented negatives or complex numbers to explain that concept as best as possible.
Also, complex numbers are useless when calculating headings and orientations (North, East, South, West). Again derived from the information from BetterExplained.com, instead of using cosine or sine, one can use complex numbers to find directions easily. (See the article for the actual explanation.)
I would think that using complex solutions in a quadratic simplifies a quadratic more. Instead of leaving the quadratic in its form with a negative in the discriminant, we could use i to simply it a little more and end the equation with two answers using that contain i. It’s more work but in my opinion, I think it cleans up the equation instead of leaving lots of numbers in there.