Find the roots of the equation z4 = 1 and select the correct option.

The given equation is $z^4 = 1$.
We can rewrite this as $z^4 - 1 = 0$.

Here, $a = z^2$ and $b = 1$.

The first term, $z^2 - 1$, is another difference of squares:

The second term, $z^2 + 1$, can be factored using the imaginary unit $i$, where $i^2 = -1$:

Substituting the factored terms back into the equation:

Setting each factor to zero gives the distinct roots:
$z-1 = 0 \implies z = 1$
$z+1 = 0 \implies z = -1$
$z-i = 0 \implies z = i$
$z+i = 0 \implies z = -i$

The four distinct roots are $1, -1, i, -i$.

A. $(1, -1, i, 2i)$
B. $(3, 2, 1, -2)$
C. $(1, -1, i, -i)$
D. $(i, -2i, -3i, -4i)$

The calculated roots match option C.

The final answer is $\boxed{\text{C. } (1, -1, i, -i)}$.