- #1
cragar
- 2,552
- 3
Homework Statement
1/((i-s)^2)) how do i rationalize this , would i multpiy top and bottom by
(i+s)^2
Rationalizing Complex Denominators for Scientists
- Thread starter cragar
- Start date
In summary, the conversation discusses how to rationalize a complex number expression, specifically 1/((i-s)^2). The correct term for this process is "rationalize" and it involves making the denominator a real and possibly rational number. By multiplying the expression by the conjugate of the denominator, the denominator is rationalized and the expression is put into standard form.
1/((i-s)^2)) how do i rationalize this , would i multpiy top and bottom by
(i+s)^2
- #2
tiny-tim
Science Advisor
Homework Helper
- 25,839
- 258
cragar said:
(rationalize? anyway …)
Yup!
- #3
cragar
- 2,552
- 3
k thank-you
- #4
Unit
- 182
- 0
tiny-tim said:
By the way, what is the proper term? (assuming "rationalize" is not)
- #5
symbolipoint
Homework Helper
Education Advisor
Gold Member
- 7,412
- 1,876
"Rationalize" is the correct vocabulary for what you wanted.
- #6
tiny-tim
Science Advisor
Homework Helper
- 25,839
- 258
Unit said:
Hi Unit! Hi symbolipoint!
Well, "rationalize" means to make rational, which this doesn't, neither in the English nor in the mathematical sense.
It actually puts a complex number into the standard x + iy form, so I'd prefer to say "put into standard form" …
however … now you raise the point, I see that http://hyperphysics.phy-astr.gsu.edu/hbase/cmplx2.html#c2 and others do say "rationalize" … I wonder why?
- #7
Mentallic
Homework Helper
- 3,802
- 95
But it's asking to rationalize the denominator which is achieved. The denominator becomes real, and possibly rational depending on the value of s.
- #8
Дьявол
- 365
- 0
For ex. 1/i where i is complex number. By multiplying with i / i you get i / i2 = i / (-1), which makes the denominator real number (also rational) since I can write (-1) as (-1)/1 and the final equation would be i / (-1) / 1. Now the denominator is rational and I rationalize the equation.
Regards.
Regards.
FAQ: Rationalizing Complex Denominators for Scientists
What is the concept of "Rationalizing the denominator"?
Rationalizing the denominator is the process of removing radicals or irrational numbers from the denominator of a fraction. This is done in order to simplify the fraction and make it easier to work with.
Why is it important to rationalize the denominator?
Rationalizing the denominator is important because it allows us to work with fractions more easily. It also helps us to compare and perform operations on fractions more accurately.
What are the steps involved in rationalizing the denominator?
The steps to rationalize the denominator include: 1) Identify the radical in the denominator; 2) Multiply the numerator and denominator by the conjugate of the radical; 3) Simplify the resulting fraction if possible; 4) Repeat the process if there are still radicals in the denominator.
Can any denominator be rationalized?
No, not all denominators can be rationalized. Only denominators that contain radicals or irrational numbers can be rationalized. Fractions with rational denominators do not need to be rationalized.
What are the benefits of rationalizing the denominator?
Rationalizing the denominator allows us to simplify fractions and make them easier to work with. It also helps us to compare and perform operations on fractions more accurately. Additionally, rationalizing the denominator is often necessary in order to solve certain mathematical equations or problems.