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

Algebra ->  Radicals -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!




Which is to say:







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:



The arithmetic is left as an exercise for the student.


John

My calculator said it, I believe it, that settles it