SOLUTION: Jane comes up to you with the following dilemma: She read in the book that {{{i^2 = -1}}} but she did some math on her own and came up with the following: {{{i^2=i*i=sqrt(-1)

Algebra ->  Radicals -> SOLUTION: Jane comes up to you with the following dilemma: She read in the book that {{{i^2 = -1}}} but she did some math on her own and came up with the following: {{{i^2=i*i=sqrt(-1)      Log On


   



Question 184754: Jane comes up to you with the following dilemma:
She read in the book that i%5E2+=+-1 but she
did some math on her own and came up with the following:

Her question is how can this be? Write a paragraph explaining how to resolve this dilemma for her.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Jane comes up to you with the following dilemma:
She read in the book that i%5E2+=+-1 but she
did some math on her own and came up with the following:

Her question is how can this be? Write a paragraph explaining how to resolve this dilemma for her.

The violation of rules for multiplying under
radicals is violated in this step above:

sqrt%28-1%29sqrt%28-1%29=sqrt%28%28-1%29%28-1%29%29

That is incorrect.

When multiplying two square roots, we can
only multiply POSITIVE numbers under square
root radicals, NEVER negative numbers. 
If a negative number is under a square root
radical such as sqrt%28-7%29, we must first 
write it as i%2Asqrt%287%29 so that there will 
only be a positive number under the square root
radical.  And we simply learn that i%5E2=i%2Ai=-1 
by definition.

Edwin