1.$\displaystyle x^3-y^3=27$

The question says, what is the number of solutions to this equation in the field of complex numbers?

The choices are

a) 1

b) 2

c) 3

d) infinitely many

I have no clue to this one.

2.And here's another one:

For any real number x, $\displaystyle \sqrt{\sqrt{-x}}$ is equal to

a) +x

b) -x

c) complex

d) pure imaginary

Writing it in the form $\displaystyle ({-x}^{1/2})^{1/2}$, we can simplify it to $\displaystyle \sqrt[4]{-x}$

Which shows that the number is not real (since no number to the power four would give -x). So +x and -x are eliminated. But what about the last two choices? What is the difference between complex and pure imaginary?