options: Represent and model with vector quantities.

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

Perform operations on matrices and use matrices in applications.

Use properties of rational and irrational numbers.

Reason quantitatively and use units to solve problems.

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

Perform arithmetic operations with complex numbers.

Extend the properties of exponents to rational exponents.

Represent complex numbers and their operations on the complex plane.

Perform operations on vectors.

Use complex numbers in polynomial identities and equations.

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

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.
problem_activity: Task
Let $z = 1 + i$ where $i^2 = -1$.   Calculate $z^2, z^3,$ and  $z^4$.
Graph $z, z^2, z^3,$ and  $z^4$ in the complex plane.  What do you notice about the positions of these  numbers?
What is $z^{100}$?  Explain.


correct_option_index: 6