Introduction to i and Imaginary Numbers

Learn more: http://www.khanacademy.org/video?v=ys...
Introduction to i and imaginary numbers

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  Education

[Binnoy Panicker]

Lets say you are facing towards the East.

Now suddenly you shift by 90 degees and start facing the North.

You just term this position as "i" which indicates rotation by 90 degrees from the start point.

Now lets say again you rotate by 90 degree. You are now facing the west. You term this as -1 since your direction is negative as compared to the start point.Hence i*i = -1 which means rotating twice by 90 degrees makes you point in the opposite direction.

Binnoy

Visualizing Maths.

[Binnoy Panicker]

i = rotation by 90 deg

-1 = rotation by 180 deg

-i = rotation by 270 deg.

-1 x i x i = rotation by (180+90+90) = rotation by 360 deg. Also -i x i = rotation by (270 + 90) = rotation by 360 deg. '1' means after a complete rotation, the object has now come back to start .

This happens at 0 deg, 360 deg, 720 deg, 1080 deg... so on.

Hope this helps

Binnoy

Visualizing maths

A book beyond the formulas

[Leonard Curly]

What about fractional powers? :)

[Binnoy Panicker]

'i' is just a way by which mathematicians could denote that the object is rotated or inclined. For example if a stick is kept horizontal its length say is '5'. Now if the same stick is kept vertical, can we measure it on the same number line? No right.

For this reason, mathematicians used complex numbers to just denote that the object is just rotated now, so they denoted it as 5i.

Hope this helps,

Binnoy

Visualizing Maths

A book beyond formulas.

[Binnoy Panicker]

Imagine a surface of water. Now if you hit this surface with one hand, the impact is (impact)^1.

If the surface is hit with two hands, the impact will be (impact)^2.

With three hands, the impact = (impact)^3.

But with no hands, there is no impact. So now the surface of water remains 'as it is'. In maths 'as it is' is denoted by the number '1'.

Hence (impact)^0=1.

Thus (anything)^0 actually denotes absence of that "anything", thus keeping the surroundings "as it is".

Binnoy

Visualizing maths.

[flawns]

confusing....

[Ficon0700]

yep..

Must watch right after this video....

=oENQ2jlHpfo

[AeroSpace1210]

Look at it this way. What is 2^4= 16, 2^3=8, 2^2=4, 2^1=2. What do you notice. Hopefully you noticed that to go from 2^4 to 2^3 you had to divide by 2. To go from 2^3 to 2^2 you had to divide by 2 and to go from 2^2 to 2^1 you also divide by two. So following this pattern 2^0= 1. Another way to look at it is through the law of exponents. x^y/x^z= x^y-z. Hope that helps. If you need more verification contact me on my inbox and I will make a video about it.

[convex37]

= i

[Justin Truong]

Can anyone solve i^502348121 in less than 5 seconds? ;)

[Caleb Fox]

Can someone please explain to me why anything ^0 =1