SOLUTION: 1.) Explain the relationship between radical equations and complex numbers. What are the most important things to keep in mind when working with radical equations and complex numbe
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Question 1120650: 1.) Explain the relationship between radical equations and complex numbers. What are the most important things to keep in mind when working with radical equations and complex numbers?
2.) We know that the square root of -1 is i. Going a bit further: what is the square root of i? [Hint: the square root of i will be a complex number, of the form a + bi. So, (a+bi)*(a+bi) = i. FOIL the left side, come up with equations relating a and b, and see if you can solve the system.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
^2\ =\ i)
Which is to say:
(a\ +\ bi)\ =\ 0\ +\ i)
\ +\ 2abi\ =\ 0\ +\ i)
Since 
if and only if 
and 
It must be true that:
and
So 
and then 
Hence 
The positive square root of 
is then 
Check the answer:
^2\ =^?)
The arithmetic is left as an exercise for the student.
John
My calculator said it, I believe it, that settles it
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