UNIT 1

Perform arithmetic operations with complex numbers.

Use complex numbers in polynomial equations

Solve equations and inequalities in one variable

Extend the properties of exponents to rational exponents

MGSE9-12.N.CN.1 Understand there is a complex number i such 2 that i = −1, and every complex number has the form a + bi where a and b are real numbers.

MGSE9-12.N.CN.2 Use the relation i = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

MGSE9-12.N.CN.3 Find the conjugate of a complex number; use the conjugate to find the quotient of complex numbers.

MGSE9-12.N.CN.7 Solve quadratic equations with real coefficients that have complex solutions by (but not limited to) square roots, completing the square, and the quadratic formula.

MGSE9-12.N.CN.8 Extend polynomial identities to include factoring with complex numbers.

MGSE9-12.A.REI.4 Solve quadratic equations in one variable. MGSE9-12.A.REI.4b Solve quadratic equations by inspection 2 (e.g., for x = 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation (limit to real number solutions).

MGSE9-12.N.RN.1 Explain how the meaning of rational exponents follows from extending the properties of integer exponents to rational numbers, allowing for a notation for radicals in terms of rational exponents.

MGSE9-12.N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

• What is a complex number and how do you simplify them?

• How do you add, subtract, and multiply complex numbers?

• What is a conjugate and how do you use it to divide complex numbers?

• How do you solve a quadratic equation that has complex solutions?

• How do I factor polynomials that have complex solutions?

• How do I solve quadratic equations?

• How do I solve quadratic equations by inspection?

• How do you extend the properties of exponents to rational exponents?

Complex number

Complex conjugate

Complex plane

Real number

Imaginary number

Solution

x-intercept

Roots

Zeros

Square Root Method

Quadratic Formula

Complex solutions

Binomial expression

Polynomial

Trinomial

Rational exponents

Expression

Rational expression

Rational number

Irrational number

Whole number

MGSE9-12.N.CN.7

Solve for x:

a. using square root method b. by completing the square c. using the quadratic formula

x² + 8 = 0

MGSE9-12.N.CN.8

Rewrite x ^2+ 4 by factoring with complex numbers.

(x + 2i)(x – 2i)

MGSE9-12.A.REI.4

Solve for x:

x² + 3x − 12 = 6

x = -6 and x = 3

MGSE9-12.A.REI.4b Solve for x:

7x² + 1 = 29

{2, −2}

MGSE9-12.N.RN.1 Which example explains the definition of rational exponents by extending the properties of integer exponents to radical expressions?

a. = = = y b. = = c. d.

MGSE9-12.N.RN.2 Which expression is equivalent to + - ? a. 3 + 2x – 5 b. 3 + 2 - 5 c. 3 + 2 - 5 d. 3 + 2 - 5