options: Perform arithmetic operations with complex 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 operations on vectors.

Use properties of rational and irrational numbers.

Use complex numbers in polynomial identities and equations.

Reason quantitatively and use units to solve problems.

Perform operations on matrices and use matrices in applications.

Represent complex numbers and their operations on the complex plane.

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.

Represent and model with vector quantities.

Extend the properties of exponents to rational exponents.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
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: 0