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### Math

## Common Core Math

# High School: Number and Quantity: The Complex Number System

Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real.

- Classify complex numbers
- Classifying complex numbers
- i as the principal root of -1
- Intro to complex numbers
- Intro to complex numbers
- Intro to the imaginary numbers
- Intro to the imaginary numbers
- Parts of complex numbers
- Powers of the imaginary unit
- Powers of the imaginary unit
- Powers of the imaginary unit
- Simplify roots of negative numbers
- Simplifying roots of negative numbers

Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

- Add & subtract complex numbers
- Adding complex numbers
- Complex number operations review
- Multiply complex numbers
- Multiply complex numbers (basic)
- Multiplying complex numbers
- Multiplying complex numbers
- Powers of the imaginary unit
- Powers of the imaginary unit
- Powers of the imaginary unit
- Subtracting complex numbers

Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

- Absolute value of complex numbers
- Complex number absolute value & angle review
- Complex number conjugates
- Complex number conjugates
- Complex numbers with the same modulus (absolute value)
- Divide complex numbers
- Dividing complex numbers review
- Intro to complex number conjugates
- Modulus (absolute value) of complex numbers

Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

- Absolute value & angle of complex numbers
- Angle of complex numbers
- Complex number absolute value & angle review
- Complex number forms review
- Complex numbers from absolute value & angle
- Complex plane and polar form
- Converting a complex number from polar to rectangular form
- Graphically add & subtract complex numbers
- Plot numbers on the complex plane
- Plotting numbers on the complex plane
- Polar & rectangular forms of complex numbers
- Polar & rectangular forms of complex numbers
- The complex plane

Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

- Complex number conjugates
- Complex number equations: x³=1
- Complex number polar form review
- Dividing complex numbers in polar form
- Graphically add & subtract complex numbers
- Graphically multiply complex numbers
- Intro to complex number conjugates
- Multiply & divide complex numbers in polar form
- Multiplying complex numbers graphically example: -1-i
- Multiplying complex numbers graphically example: -3i
- Multiplying complex numbers in polar form
- Powers of complex numbers
- Taking and visualizing powers of a complex number
- Visualizing complex number multiplication
- Visualizing complex number powers

Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

Solve quadratic equations with real coefficients that have complex solutions.

Extend polynomial identities to the complex numbers.

Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.