standard_description: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
problem_activity: Task
Working with complex numbers allows us to solve equations like $z^2 = -1$
which cannot be solved with real numbers.  Here we will investigate complex numbers which arise as square roots of certain complex numbers.
Find all complex square roots of -1, that is, find all numbers $z = a + bi$ which satisfy $z^2 = -1$.
Find all complex square roots of 1.
Which complex numbers satisfy $z^2 = i$?


aligns: no