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Thank you for telling us the mistake :D

Pie is a kind of food.

I think you mean 'pi'

'pi' is the ratio of the circumference of any circle to the diameter of the same circle.

~The smartest cookie in the world

Ta(7) is still not found yet. Maybe we will wait for the super mathematicians for few more years and they get the value of it.

So far, the ever-found biggest Taxicab number is 

\(\text{Ta}(6)=\;24153319581254312065344\\ =582162^3 + 28906206^3\\ =3064173^3+ 28894803^3\\ = 8519281^3 + 28657487^3\\ =16218068^3 + 27093208^3\\ = 17492496^3 + 26590452^3\\ =18289922^3 + 26224366^3\)

Enough mind-blowing isn't it?

~The smartest cookie in the world

Maybe.

Let's think about \((i^i)^i\) which is \(e^{-i\pi/2}=e^{1/2\cdot\ln(-1)}=\left(e^{\ln(-1)}\right)^{1/2}=\sqrt{-1} = i\)

Then think about \(\left(\left(i^i\right)^i\right)^i\\ \) which is

\(i^i = e^{-i\pi/2}\)

We just go in imaginary -> real -> imaginary -> real -> ......... circles.

We can conclude that:

\(\left(\left(i^i\right)^{.......}\right)^i\text{ with odd number of }i = i\\ \left(\left(i^i\right)^{.......}\right)^i\text{ with even number of }i = e^{-\pi/2}\)

\(\sqrt{200} \rightarrow \sqrt{100\times2} \rightarrow \sqrt{100} \times \sqrt{2} \rightarrow 10\sqrt{2} \)

Thank you!! That is really awesome!! 

x²+16x-225=0

(x-9)(x+25)

x=9,-25

Thank you for answering :D

The Canadian dollar coin is often called a loonie. The loonie is a regular 11-gon. What is the measure of each interior angle of an 11-gon? Round to the nearest tenth of a degree.

180(11-2)/11 = 147.2727272727272727 degrees 

Hi Max,

I know you are the smartest cookie in the world.

Everyone here knows it too.

So please do not do all of anyone's homework.

How much do you think someone learns when you do all their homework for them ?

Also,

When you post an answer can you be sure to include some ordinary type in it somewhere.

If it only has LaTex then other people cannot hyperlink into it from the answer page.

I usually get around this by copying the original question in first.

If the question is all latex then I would make up some thing to put first.  :)

I am not referring to this answer, I am just talking about answers in general :)

Thanks :)

This question looks like nonsense to me.

(7ab)1/2

\((7ab)^{1/2}=\sqrt{7ab}\\ or\\ 7ab*1/2= 7ab/2\)

Try watching this clip.

It is a bad question but the only possible answer out of those is  A

(2835-2765)/2765*100 = 2.5316455696202532         2.5%

(2835-2765)/2835*100 = 2.4691358024691358          2.5%

Perhaps you would be interested in quaternions Max (see https://en.wikipedia.org/wiki/Quaternion for example).  These extend the concept of complex numbers.

I had a thought,

Any number divided by itself =1,  even complex numbers.

and

If you multiply a complex number by its conjugate you get a real number too :)

Jake ate 1 and a half pizza out of ten pizza slices

4598.12 plus 900= 5498.12 I got it right

99 is a number between 98 and 100 and doesn't have an exclamation mark after it

I have posted an answer on the original thread :)

The answer is 19 kid

Hi Max,

How about:

\(i^i=real\;number\)

proof:

\(i^i=e^{lni^i}=e^{ilni}\\ \qquad \qquad \text{For complex logs}\\ \qquad \qquad ln(z)=ln|z|+i*arg(z)\\ so\\ ln(i)=ln|i|+i*arg(i)\\ \qquad =ln(1)+i*\frac{\pi}{2}\\ \qquad =i*\frac{\pi}{2}\\~\\ so\\ i^i=e^{lni^i}\\ \:\:\:=e^{i*lni}\\ \:\:\:=e^{i*i*\frac{\pi}{2}}\\ \:\:\:=e^{-1\frac{\pi}{2}}\\ \:\:\:=e^{\frac{-\pi}{2}}\\ \)

So maybe we start going in circles    

Use atan

arctan is the same as inverse tan :)