Why is i^4 not -i?

[UglyCasanova]

Ok, so I was thinking about this today for some reason.

i^0=1
i^1=i
i^2=-1
i^3=i^2 * i=-1 * i = -i
i^4=i^2 * i^2= -1 * -1= 1

But why not...

i^4=i^3 * i = -i * i = -i

And I've read the rotational explanation of it, I get it, makes sense. But why could you not break i^4 down how I did the second time and end up with -i?

I'm sure there's an explanation and probably what it is is that I need to revisit exponents. Been a while since I've sat through a math class.

 

[OCGuy]

Because you sit to pee.

 

[UglyCasanova]

Nm, that would be -i^2 which would be 1. Crisis averted.

 

[bhagan]

wouldn't that last one get you to -i^2, and thus 1

 

[sao123]

i^4=i^3 * i = -i * i = -i

-i * i = (-1) * i * i = (-1) * i^2 = (-1) * (-1) = 1

 

[IAteYourMother]

This reminds me of when I think too hard and then start questioning why certain words sound really weird

 

[MovingTarget]

Consider the "Wheel of Fun" back from ye olde days of Algebra. i=√(-1). Multiply i by itself and you get i^2=-1. Multiply i^2 by i and you get i^3=i^2 * i = -1 * i = -i. Multiply the result by i again and you get i^4 = i^3 * i = -i * i = -1 * i^2 = -1 * -1 = 1. Multiply by i again and you get i^5 = i^4 * i = 1 * i = i. The cycle repeats. Your teacher probably represented this using a wheel turning counterclockwise, because, any number plotted in the complex plane, when multiplied by i, undergoes a counterclockwise rotation of 90º. Four of these transformations gets you back where you started. Ermagherd!

 

[disappoint]

Ok, so I was thinking about this today for some reason.

i^0=1
i^1=i
i^2=-1
i^3=i^2 * i=-1 * i = -i
i^4=i^2 * i^2= -1 * -1= 1

But why not...

i^4=i^3 * i = -i * i = -i

And I've read the rotational explanation of it, I get it, makes sense. But why could you not break i^4 down how I did the second time and end up with -i?

I'm sure there's an explanation and probably what it is is that I need to revisit exponents. Been a while since I've sat through a math class.

Bolded is where you madeth the mistake. -i * i doth not equal -i.

 

[Ken g6]

(ay)^4. Ya no tengo matemáticas.

 

[brianmanahan]

2 math fail threads in 1 day

too much

 

[dighn]

2 math fail threads in 1 day

too much

this isnt real math

 

[brianmanahan]

this isnt real math

well, it's imaginary numbers

but it is totally real

especially useful in EE

 

[gorcorps]

You multiplied ... Poorly

 

[Arcadio]

This should teach the OP that math is flawless.

 

[bommy261]

well, it's imaginary numbers

but it is totally real

especially useful in EE

methinks hes being sarcastic.

 

[brianmanahan]

methinks hes being sarcastic.

i never know around here

i made the mistake of going to P&N a few times, now my meter is broken