few_shots: Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Mathematical concept/skill options: 
A. Prove and apply trigonometric identities.
B. Model periodic phenomena with trigonometric functions.
C. Interpret functions that arise in applications in terms of the context.
D. Build a function that models a relationship between two quantities.
E. Define, evaluate, and compare functions.
F. Use functions to model relationships between quantities.
G. Understand the concept of a function and use function notation.
H. Analyze functions using different representations.
I. Extend the domain of trigonometric functions using the unit circle.
J. Interpret expressions for functions in terms of the situation they model.
K. Build new functions from existing functions.
L. Construct and compare linear and exponential models and solve problems.


Your response, in json format:
{
  "explanation": "This problem applies trigonometric identities, including the angle addition formula for cosine.",
  "answer": "A"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001894

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

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

Perform arithmetic operations with complex numbers.

Use complex numbers in polynomial identities and equations.

Represent and model with vector quantities.

Perform operations on vectors.

Reason quantitatively and use units to solve problems.

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

Extend the properties of exponents to rational exponents.

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

Use properties of rational and irrational numbers.

Represent complex numbers and their operations on the complex plane.

Perform operations on matrices and use matrices in applications.

Apply and extend previous understandings of numbers to the system of 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: 2