from auditorium import Show
from auditorium.show import Context

show = Show('My Show')


@show.slide
def intro(ctx):
    """
    ### Mathematical Foundation of Algorithms

    Algebra - Complex Numbers
    """


@show.slide
def score(ctx):
    """
    Each day homework will have a value of 12 points.

    - Homework: 12 * 12 = 144 points
    - Final Exam: 56 points (Mandatory participation)
    - Maximum grade: 180 points
    """


@show.slide
def complex_number(ctx):
    """
    ## Complex numbers

    $$\sqrt{-1} = ?$$
    """


@complex_number.slide
def complex_number_inner_1(ctx):
    """
    ## Complex numbers

    $$i^2 = -1$$
    $$i = \sqrt{-1}$$
    """


@complex_number.slide
def complex_number_inner_2(ctx):
    """
    ## Complex numbers

    $$i^2 = -1$$
    $$i = \sqrt{-1}$$
    """


@complex_number.slide
def introduction_to_complex(ctx):
    """
    ## Introduction to complex numbers
    """


@complex_number.slide
def implement_complex_number(ctx):
    """
    ## Implement complex number
    """


@show.slide
def triangles(ctx):
    """
    ## Draw triangles
    """


@show.slide
def complex_number_inner(ctx):
    """
    ## Draw complex fractals
    """


@ show.slide
def homework(ctx):
    """
    Homework
    """


@homework.slide
def task_1(ctx):
    """
    `**`

    Implement remaining methods of complex number:

    - substraction
    - multiplication
    - division
    - exponentiation
    """


@homework.slide
def task_2(ctx):
    """
    `**`

    Given a polynomial of degree 2:

    $$a \cdot x^2 + b \cdot x + c$$

    Compute the roots of this polynomial
    """


@homework.slide
def task_3(ctx):
    """
    `***`

    Prove that:

    $$(\\cos \\theta + i \\sin \\theta)^n = \\cos n \\theta + i \\sin n \\theta$$
    """


@homework.slide
def task_4(ctx):
    """
    `**`

    1. Given a complex number in rectangular form, convert to polar form.
    2. Given a complex number in polar form, convert to rectangular form.
    """


@show.slide
def bye(ctx):
    """
    ### Mathematical Foundation of Algorithms

    Algebra - Complex Numbers
    """