Complex Roots (Imaginery Numbers) Answers With Sharp El-W519X

In summary, the calculator is displaying fewer DP than it stores for it's calculations and this is causing problems when solving for imaginary roots.
  • #1
sammy134
1
0
Ive had this problem with the calculator since I bought it. It might be that the calculator does not have enough implemented functions to pull it off or I am missing something. It happens when I am solving for imaginery roots.

Example: y^2 + y^1+y = 0.

I go to mode, and select 6(equation) and than select 2 (quadratic). I put in a = 1, b = 1, c = 1. I get the answer -0.5 +/- 0.866025403i

Now I understand that this is the correct answer that's not my problem. I am currently taking Differential Equations math course and when I am finding the homogenous answer to a solution with complex roots I need to be able to state the answer in FRACTION form. The correct fraction form is SQRT(3)/2. Now normally if I type in SQRT(3)/2 I change between 0.866025403 and SQRT(3)/2. But if I type in 0.866025403 and press =, I can't change to SQRT(3)/2 because its not the exact amount of decimals. I need to be able to give the answer as -0.5 +/ SQRT(3)/2. So that I can use it to give the homogenous answer to the solution being e^-1/2*(c1*cos(SQRT(3)/2) + (c2*sin(SQRT(3)/2). Usually hitting the "change" button rotates between the Fraction form and the decimal form of an answer, but I can't use change button under the equation, quadratic solver. It does nothing when I hit it.

Now my question is, 1) is there anything else that I can do to fix my problem, and 2) if there is nothing I can do, is there a more advanced brand of SHARP that I can buy, maybe one with more implemented fuctions, if that is the problem. Keep in my mind that it still has to be not advanced as a graphing because I need to be able to use it on exams.

Thank you!
 
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  • #2
The calculator is displaying fewer DP than it stores for it's calculations.
All calculators will have this problem because they would otherwise have to be able to guess which fraction your string of decimals is approximating. (does it make the right guess for 0.3333333333?)

There are computers capable of that sort of thing - what you need is something advanced enough to be self-aware. These things can be quite pricey to maintain and hard to program reliably, but well worth the effort. Fortunately almost all of us are born with one.

Enjoy :)
 

What are complex roots?

Complex roots, also known as imaginary roots, are solutions to an equation that involve the use of the imaginary number i, which is defined as the square root of -1.

How do you solve equations with complex roots?

To solve an equation with complex roots, you must first rewrite the equation in the form a + bi, where a and b are real numbers and i is the imaginary unit. Then, you can use various algebraic techniques, such as factoring and the quadratic formula, to solve for the roots.

What are the properties of complex roots?

Complex roots come in pairs, known as conjugate pairs. This means that if one root is a + bi, the other root is a - bi. Additionally, complex roots can be added, subtracted, multiplied, and divided using the same rules as real numbers.

How are complex roots useful in science?

Complex roots are useful in science because they allow us to solve equations and model real-world phenomena that involve quantities that cannot be expressed using only real numbers. They are also essential in fields such as electrical engineering, quantum mechanics, and signal processing.

What is the role of the imaginary unit in complex roots?

The imaginary unit i is crucial in complex roots because it allows us to represent and work with numbers that are not possible to express using only real numbers. Without the imaginary unit, many important equations and models in science would not be possible.

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