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

Use complex numbers in polynomial identities and equations.

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

Represent and model with vector quantities.

Perform operations on vectors.

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

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

Use properties of rational and irrational numbers.

Reason quantitatively and use units to solve problems.

Perform arithmetic operations with complex numbers.

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

Extend the properties of exponents to rational exponents.

Perform operations on matrices and use matrices in applications.

Represent complex numbers and their operations on the complex plane.
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: 9