Complex Numbers, Part 5 - The Imaginary Unit

What 'i' is, and the pattern that appears when raising i to a power. Part of the Algebra 2 series on complex numbers. By Derek Owens. Distance learning courses are available at http://www.derekowens.com

Category:

Education

Tags:

• complex numbers
• complex
• imaginary numbers
• imaginary
• imaginary unit
• raising i to a power
• derek owens
• math
• homeschool math
• homeschool.

[fireluigi12]

what if the exponent of i is negative?

[derekowens]

@fireluigi12 The same pattern holds, going in the opposite direction.

i^0 = 1

i^-1 = -i

i^-2 = -2

i^-3 = i

and so on

[fireluigi12]

@derekowens is i^-2 really -2, or is it -1?

[derekowens]

@fireluigi12 Whoops, typing too fast. Yes, it is -1. Sorry, and thanks.

[SaurabhOKumar]

He is Just using the concept of VEDIC MATHEMATICS here, WITHOUT telling ANYONE OF US or Confessing about it, thats' how guys like HIM end up being ETHINICALLY GAY even to their forefathers; and BRAINWASH others to that THiNKING that things happen only through them, whose ansestors stole others' concepts without getting an authorization or rights. No Confession AT ALL in order to florish the names of his mENTALLY SICK FOREFATHERS!

[derekowens]

@SaurabhOKumar Sorry, but I'm not familiar with Vedic Mathematics. Nothing ethnic here, nor gay either, just some math theory and some intellectual contributions by Gauss. And yes, ideas come from a variety of places, but I'm not aware Gauss stealing any from anyone.

[fuedebe]

i can just sit here and not go to class anymore. you lecture pretty well.

[realrockstar786]

thank u very much.it really helped lot.

[wingsofbala]

super....



[GearZNet]

My method is based on the cycle of real numbers i^2 = -1 and i^4 = 1. I call it " KEEPIN IT REAL!" :) If an EVEN exponent IS divisible by 4 then => +1 BUT If NOT => -1. Secondly, any ODD exponent is either -i or +i. EXAMPLE: [A] i^27 is i^26 * i => => 26 is NOT divisible by 4 so RESULT = -i. [B] i^29 = i^28 * i SO 28 IS divisible by 4 so result = +i ... SO No remainders are needed :)

Derrell Wiliams

[3bood1st]

nice jop keep it up :)

[Anonymystik]

... the imaginary parts canceled themselves and the only remaining part was the real one. Therefore, this has a point to count with these "unreal" numbers. Furthermore, lots of problems can be solved more easily by using them, instead of trying to avoid them. As for the example, in physics, complex numbers are used to deal with RLC circuits. But aren´t all the numbers just only the abstraction? You know, what means "three apples" or "three chairs", but what exactly means word "three" ?

[Anonymystik]

It is an interesting question, if we should take complex numbers just like the other numbers. I think, it is just an abstraction, maybe useful (not only in mathematics, but also in physics), but it is just only a different way how to solve some problems. Interesting is, that complex numbers were discovered, when Rafael Bombelli tried to solve a cubic equations, which had 3 real solutions. He found out, that the formula he was using lead to complex numbers, although at the end...