Question: 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?

Hint: First, define a radical equation, and give an example. Then, define the imaginary unit and complex numbers, and give examples. Finally, tell how a radical equation might have complex solutions.

Challenge 1: What are the four solutions to x⁴ = 1? (Hint: two are real, and two are complex. One approach is to rewrite the equation, and then factor. To factor, think back to Discussion Question 10, Difference of Squares).

Challenge 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.]