# Tedious Simplification: Show expression is real

• JolleJ
In summary: I just wanted to know if there was a technique or function in Maple or Mathematica that could help me simplify it further.
JolleJ
After doing A LOT of simplification on a complicated expression I am now at a point where my own skills can't take me any further.

My problem is that I have an expression, which I am almost certain must be real, but it contains the imaginary units here and there. I have tried using Maple and Mathematica with different assumptions, but it does not simplify very much.

Now, I do not expect you to do my tedious algebra. However, I was hoping that one of you might know of a technique (in Maple/Mathematica/Hand) that could help me?

My expression is this:

${\frac {\sqrt [3]{2}n \left( -1+n \right) \left( -1+2\,n \right) \left( 2\,\sqrt [3]{-2}+4\,\sqrt [3]{-2} \left( -1+n \right) n+ \left( -1-2\,n \left( 1+ \left( -3+n \right) n \right) +i\sqrt {1-16 \,n+44\,{n}^{2}-44\,{n}^{3}+28\,{n}^{4}-24\,{n}^{5}+12\,{n}^{6}} \right) ^{2/3}-i\sqrt {3} \left( -1-2\,n \left( 1+ \left( -3+n \right) n \right) +i\sqrt {1-16\,n+44\,{n}^{2}-44\,{n}^{3}+28\,{n}^{4 }-24\,{n}^{5}+12\,{n}^{6}} \right) ^{2/3} \right) }{\sqrt [3]{-1-2\,n \left( 1+ \left( -3+n \right) n \right) +i\sqrt {1-16\,n+44\,{n}^{2}- 44\,{n}^{3}+28\,{n}^{4}-24\,{n}^{5}+12\,{n}^{6}}} \left( -8+16\,n \right) }}$
where n is an interger larger than 1.

as you can see the same terms appear many places.Any help will be greatly appreciated.

Maple format:
Code:
2^(1/3)*n*(-1+n)*(-1+2*n)*(2*(-2)^(1/3)+4*(-2)^(1/3)*(-1+n)*n+(-1-2*n*(1+(-3+n)*n)+I*sqrt(1-16*n+44*n^2-44*n^3+28*n^4-24*n^5+12*n^6))^(2/3)-I*sqrt(3)*(-1-2*n*(1+(-3+n)*n)+I*sqrt(1-16*n+44*n^2-44*n^3+28*n^4-24*n^5+12*n^6))^(2/3))/((-1-2*n*(1+(-3+n)*n)+I*sqrt(1-16*n+44*n^2-44*n^3+28*n^4-24*n^5+12*n^6))^(1/3)*(-8+16*n))

Mathematica format:
Code:
(2^(1/3) (-1 + n) n (-1 + 2 n) (2 (-2)^(1/3) +
4 (-2)^(1/3) (-1 + n) n + (-1 - 2 n (1 + (-3 + n) n) +
I Sqrt[1 - 16 n + 44 n^2 - 44 n^3 + 28 n^4 - 24 n^5 +
12 n^6])^(2/3) -
I Sqrt[3] (-1 - 2 n (1 + (-3 + n) n) +
I Sqrt[1 - 16 n + 44 n^2 - 44 n^3 + 28 n^4 - 24 n^5 +
12 n^6])^(2/3)))/((-8 + 16 n) (-1 - 2 n (1 + (-3 + n) n) +
I Sqrt[1 - 16 n + 44 n^2 - 44 n^3 + 28 n^4 - 24 n^5 + 12 n^6])^(
1/3))

Last edited:
Here's one idea:

If the number is pure real, then you can multiply the i's by -1 and after this, you should have the same number as before.

Thanks. Yes, that is a good idea. However, the expression is so complicated that it doesn't really help. I can't show the expressions are the same.

And actually, which I should have clarified, I do need the simplified expression.

## 1. What is "Tedious Simplification: Show expression is real"?

"Tedious Simplification: Show expression is real" is a scientific concept that refers to the process of simplifying complex expressions or equations to better understand their underlying reality. It involves breaking down a complicated equation or concept into smaller, more manageable parts in order to gain a deeper understanding of its meaning.

## 2. Why is "Tedious Simplification: Show expression is real" important in science?

"Tedious Simplification: Show expression is real" is important in science because it allows scientists to better understand and explain complex phenomena. By simplifying equations and expressions, scientists can identify patterns, relationships, and underlying principles that would otherwise be difficult to see. It also helps to make complex concepts more accessible and easier to communicate to others.

## 3. How is "Tedious Simplification: Show expression is real" different from oversimplification?

While both "Tedious Simplification: Show expression is real" and oversimplification involve simplifying complex concepts, they are different in their approach and purpose. "Tedious Simplification: Show expression is real" aims to break down a complicated concept in order to better understand its underlying reality, while oversimplification involves reducing a concept to the point where it loses its accuracy and meaning. "Tedious Simplification: Show expression is real" is a scientific method, while oversimplification can lead to misunderstandings and incorrect conclusions.

## 4. What are some common techniques used in "Tedious Simplification: Show expression is real"?

There are several techniques that can be used in "Tedious Simplification: Show expression is real". These include factoring, substitution, simplifying fractions, and using properties of exponents and logarithms. Other methods may also be used depending on the specific equation or expression being simplified.

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"Tedious Simplification: Show expression is real" can benefit other fields besides science by providing a method for breaking down complex concepts and making them more accessible. This can be useful in fields such as economics, engineering, and mathematics, where complex equations and theories are often used. By simplifying these concepts, they can be better understood and applied in practical situations.

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