Rationalizing Complex Denominators for Scientists

[cragar]

Homework Statement

1/((i-s)^2)) how do i rationalize this , would i multpiy top and bottom by
(i+s)^2

 

[tiny-tim]

1/((i-s)^2)) how do i rationalize this , would i multpiy top and bottom by
(i+s)^2

(rationalize? anyway …)

Yup!

 

[cragar]

k thank-you

 

[Unit]

(rationalize? anyway …)

By the way, what is the proper term? (assuming "rationalize" is not)

 

[symbolipoint]

"Rationalize" is the correct vocabulary for what you wanted.

 

[tiny-tim]

By the way, what is the proper term? (assuming "rationalize" is not)

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?

 

[Mentallic]

But it's asking to rationalize the denominator which is achieved. The denominator becomes real, and possibly rational depending on the value of s.

 

[Дьявол]

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.