Question 1113011: please solve 5/-2 + 5i
-2/-2 (5/-2 + 5i)
1/-2 ( 5/ 5i)
1/-2 ( 1/ i )
1/ -2i
2/2 ( 1 / -2i )
? I'm lost from here ? 2 /-i ?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
"Solve" doesn't make any sense. You can't solve something that does not contain a relational operator (=, >, <, etc.). So I am going to assume that you are looking to rationalize the denominator. But then I am confused by your first step. While it is certainly a valid step because you are multiplying by 1 in the form of -2 divided by itself, it doesn't really get you anywhere to do that. Further, your third line does not follow from the second.
The strategy at this point is to multiply by 1, but in the form of the conjugate of the denominator divided by itself. The conjugate of any binomial expression is formed by changing the sign between the two terms. Hence, the conjugate of your denominator,  is  . Hence:
\(\frac{-2\ -\ 5i}{-2\ -\ 5i}\))
Just like multiplying any pair of fractions: Numerator X Numerator, Denominator X Denominator. Also, the product of any binomial and its conjugate is the difference of two squares and  , so:
}\ =\ \frac{-10\ -\ 25i}{4\ -\ (-25)}\ =\ \frac{-10\ -\ 25i}{29})
John
My calculator said it, I believe it, that settles it
|
|
|
