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Ed Mack
09-10-2002, 02:27 PM
Please solve this for me (if you think it can't be done, you havn't taken maths far enough)

xx = -4

(Sorry, I can't get the superscript 2 to work :()

muckyMuckMan
09-10-2002, 11:59 PM
Hey, you're the moderator. Tell the admin to enable the superscript and subscript tags (and possibly the font tag for use with the "symbol" font). :D

Is that x^2 = -4 (this means x squared equals negative four)? If so then you'll get an imaginary number when you solve for x:


x^2 = -4
x = (+/-)sqrt(-4)
x = (+/-)2i

i is defined as sqrt(-1)
since sqrt(-1)*sqrt(4) = sqrt(-4),
you can take the sqrt(4) to get (+/-)2 and substitute sqrt(-1) for i. That's how I got the answer.

Ed Mack
09-11-2002, 05:27 PM
Ah, I get it now (I take it, this is pure maths, as apposed to real maths?)

So,

x^2 = -4
x = sqrt(-4)
x = sqrt(4) * sqrt(-1)
x = 2 * sqrt(-1)

Take sqrt(-1) as i

x = 2i

Thanks very much... I've got one of those teachers who annoys students with "Now, you can't do this, but you can if you stay with maths... I wont tell you know so I don't spoil it"...

About the tags, this UBB is going to be upgraded soon (or so we are told), and he doesn't want to add any hacks right now, as they would slow it down, and have to be re-written afterwords anyway.

muckyMuckMan
09-11-2002, 08:10 PM
Glad I can help. Heh..teachers, why can't they just tell you? Huh? :) Anywho, you should do a search for "imaginary numbers" and/or "complex numbers" for some basics and such about "i".

There's something to watch out for that I'd like to point out. Consider this:

x = sqrt(-4)*sqrt(-9)

You know if you had an equation like:

x = sqrt(-4)

You could reason that x = sqrt(-4) = sqrt(4)*sqrt(-1) = 2i, as you already know....Say...doesn't it look like I'm mulptiply -1 by 4 and putting the result under a sqrt sign when you read x = sqrt(-4) = sqrt(4)*sqrt(-1) from right to left? After all multiplying two numbers that are under a sqrt sign and putting them under one sqrt sign is perfectly legal. Like


sqrt(4)*sqrt(9) = sqrt(4*9) = sqrt(36) = 6
Or
sqrt(3)*sqrt(4) = sqrt(3*4) = sqrt(12)

Right?

But with x = sqrt(-4)*sqrt(-9) it isn't right to multiply the the two numbers under the sqrt sign to get a positive number. This is what I mean:


x = sqrt(-4)*sqrt(-9) != sqrt(-4*-9) != sqrt(36) != 6

The above is not correct because you have to first consider whether or not you could actually take the sqrt of the number under a sqrt sign before you multiply it to another number under a sqrt sign. I hope this makes sense so far. :D

What you are really supposed to do is:


x = sqrt(-4)*sqrt(-9) = sqrt(4)*sqrt(-1)*sqrt(9)*sqrt(-1)

= 2*sqrt(-1)*3*sqrt(-1) = 2i*3i = 6i^2 = 6*(-1) = -6

Since i = sqrt(-1), i^2 = -1. That's where the -1 came from in the second to last step.

Okay, sorry for talking so much. I just felt like explaining something to someone. Bye.

:D

brutfood
09-13-2002, 04:15 AM
As this is the Maths AND Physics forum (ie. not just the pure stuff) - I thought I'd point out that In engineering books, you'll see that they use the letter 'j' instead of 'i' to represent sqrt(-1).

This is so not to confuse this imaginary constant with electrical current (i).

UnderTheSun
09-13-2002, 05:04 AM
reminded me i have to revise my maths on complex numbers for exam. :D

Ed Mack
09-15-2002, 06:31 AM
Thanks, I'll hopefully be able to use that in a few years ;)