Why are there such tricks with degrees? - page 3

New comment
 
Andrey Azatskiy:

Yes, I got it. Thank you. (there's even a formula written down)

You're welcome to use it. ;)

 
Олег avtomat:

Correct solution: the solution is in the complex area.

...

Really?
 
Here we go).

I decided to limit myself to the ints and not to go into the complex area.
 
Igor Makanu:

use the formula I suggested above.

Here's the same formula:

and here is an example of how to convert double into a fraction

https://www.mql5.com/ru/forum/290279#comment_9396706

You can convert to a fraction with an odd numerator, or you can convert to an even numerator (just multiply by 2 m and n).

This is what you get:

double r1=pow(pow(5.5,3),-0.1); 
Alert("r1 = ",r1); // 0.5996408252050451


double r2=pow(pow(-5.5,3),-0.1); // m нечетное
Alert("r2 = ",r2); // nan


double r3=pow(pow(-5.5,6),-0.05);  // m четное
Alert("r2 = ",r3); // 0.5996408252050451

We get an imaginary number if we want, and we get a real number if we want. So it's enough to make the argument positive, and that's it.

The result is neither a real nor an imaginary number, but some abstract number. Who can explain this paradox? Are there any mega-supermathematicians here?

And I wonder how you can manage to get the sum of a real number and an imaginary number? I guess you have to know calculus especially well, don't you?

 
Dmitry Fedoseev:

You can convert to a fraction with an odd-numbered numerator, or you can convert to an even-numbered one (just multiply by 2 m and n).

This is what we get:

We get an imaginary number if we want, and we get a real number if we want. So it's enough to make the argument positive, and that's it.

The result is neither a real nor an imaginary number, but some abstract number. Who can explain this paradox? Are there any mega-supermathematicians here?

And I wonder how you can manage to get the sum of a real number and an imaginary number? I guess you have to know calculus especially well, don't you?

You're just being silly...

Read in your textbook what complex numbers are.

and what Re(z) and Im(z) are
 
Dmitry Fedoseev:

You can convert to a fraction with an odd-numbered numerator, or you can convert to an even-numbered one (just multiply by 2 m and n).

This is what we get:

We get an imaginary number if we want, and we get a real number if we want. So it's enough to make the argument positive, and that's it.

The result is neither a real nor an imaginary number, but some abstract number. Who can explain this paradox? Are there any mega-supermathematicians here?

And I wonder how you can manage to get the sum of a real number and an imaginary number? I guess you have to know matcad especially well, don't you?

If x<0, then the statement that x^(y*z) = (x^y)^z doesn't always make sense (the left or right hand side might just be undefined)

Otherwise, for example, one could prove the equality of the imaginary unit and the ordinary unit:

i=sqrt(-1)=(-1)^0.5=(-1)^(2*0.25)=((-1)^2)^0.25=1^0.25=1

 
Олег avtomat:

You're just being silly...

you read in a textbook what complex numbers are.

And also about what Re(z) and Im(z) are

It's you, docent, who needs to read a textbook here.

 
Aleksey Nikolayev:

If x<0, then the statement that x^(y*z) = (x^y)^z does not always make sense (the left or right hand side may simply be undefined)

Otherwise, for example, one could prove the equality of the imaginary unit and the ordinary unit:

i=sqrt(-1)=(-1)^0.5=(-1)^(2*0.25)=((-1)^2)^0.25=1^0.25=1

Above showed how a simple non-contradictory manipulation resolves this contradiction. And yes the proof of equality of unit and imaginary unit is obtained.

Let's say okay, when doesn't it make sense? When exactly?

 
Олег avtomat:

You're as stubborn as a sheep, too.

You think you know what a complex number is and you're in 7th heaven and you think there are idiots around who don't know what a complex number is? Is that your superlative achievement? You've learned some formulas, learned how to manipulate them, but you don't have a living understanding of mathematics at all.

And with matcad, you don't even seem to know how to manipulate formulas.

 
Why don't we get Perelman to help and have him straighten things out?
12345678
New comment