options: Represent complex numbers and their operations on the complex plane.

Represent and model with vector quantities.

Perform operations on matrices and use matrices in applications.

Extend the properties of exponents to rational exponents.

Perform arithmetic operations with complex numbers.

Use complex numbers in polynomial identities and equations.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Use properties of rational and irrational numbers.

Perform operations on vectors.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Compute fluently with multi-digit numbers and find common factors and multiples.

Know that there are numbers that are not rational, and approximate them by rational numbers.

Apply and extend previous understandings of numbers to the system of rational numbers.

Reason quantitatively and use units to solve problems.
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 $z^2 = i$?


correct_option_index: 4