options: Use complex numbers in polynomial identities and equations.

Perform operations on matrices and use matrices in applications.

Represent and model with vector quantities.

Perform operations on vectors.

Extend the properties of exponents to rational exponents.

Reason quantitatively and use units to solve problems.

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

Represent complex numbers and their operations on the complex plane.

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

Use properties of rational and irrational numbers.

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

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

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

Perform arithmetic operations with complex numbers.
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: 13