2^?

[Mikemk]

What is your favorite power of 2?

[Nessphoro]

The power of magic.

[VolTeK]

.5

[iansjack]

-i

[Antti]

I usually think about the bit pattern.

Code: Select all

	00000001	Quite OK
	00000100	Bad
	00001000	OK
	10000000	Nice

Let's just say 128.

[Mikemk]

-i

Wouldn't that be 1?

[AJ]

Wouldn't that be 1?

Only if i was zero and then you don't need the minus sign

[Mikemk]

I thought you meant i as in √(-1). the square root of √1 is 1, so logically -√(-1) = √1 = 1

[Nessphoro]

You can't just multiply by negative 1 to covert complex-real numbers

[iansjack]

2 to the power of -i is most definitely not 1! (And -i is most definitely not 1 either.)

[bluemoon]

Why not? 0 + i and 0 - i are valid complex numbers.

By the way, how about 2^e

[CWood]

pi-th root of 2 (2^(1/pi))

I'm sure there will be some of you who get the reference

[Griwes]

I thought you meant i as in √(-1). the square root of √1 is 1, so logically -√(-1) = √1 = 1

This is one of the most frequent problems with understanding complex numbers. i IS NOT sqrt(-1). This is NOT its definition. x = sqrt(-1) is NOT i.

i is defined as follows:

i^2 = -1

No other definition of i is correct, and all of them create the bullshit you wrote before, when you said -i = 1. -i is conceptually the same as (0, -1) in R2, which is *completely different thing* than 1, which is, again conceptually, (1, 0) in R2.


Please educate yourself on such basic things before diving into talking about it.

[AJ]

Hi,

i^2 = -1

No other definition of i is correct

i^6 = -1?

Cheers,
Adam

[Griwes]

That ain't a definition. You used the fact that i^2 is -1, which is *the* definition, and you just used that fact to write (i^2)^3 = -1, which is the same as (-1)^3 = -1.