[-10i-2(5^1/2)]/5i-(5^1/2)

Question

am supposed to rationalize this. please help!!!!!!!!!

Answer 1

It isn't clear how this is supposed to look, because the parentheses are ambiguous.

Is it supposed to be this?

-10i - 2√5
------------
  5i - √5

 

If so, then to solve it you multiply the numerator and denominator by the complex conjugate of the denominator, which is 5i + √5.  Then you get:

-10i - 2√5      5i + √5          -2(5i + √5)(5i + √5)        -2(25i² + 5√5 i + 5√5 i - √5*√5)
------------    ----------   =    -------------------------   =  -------------------------------------- =
  5i - √5         5i + √5            (5i - √5)(5i + √5)                         25i² - 5

 

-2(-25 + 5 + 10√5 i) / (-25 - 5) =

 

-2(10√5 i - 20) / (-30) =

 

-20(√5 i -2 ) / (-30) =

 

(2/3) (√5 i - 2)

 

 

But please review the calculations to make sure that you agree with everything.