Examples for

Common Core Math: High School Number & Quantity: Complex Numbers

Complex numbers are numbers of the form a + bi, where a and b are real numbers and i is defined as the imaginary unit and is equal to the principal square root of -1. High school students learn to perform arithmetic with complex numbers and to plot them in the complex plane. At advanced levels, students may also learn to represent complex numbers in terms of trigonometric functions and polar coordinates. Students will find this domain relevant to their previous studies of polynomials, as complex numbers provide solutions to polynomials with roots that cannot be found by considering only the real numbers. With knowledge of complex numbers, students can learn and apply the fundamental theorem of algebra, which states that a polynomial of degree n has exactly n complex roots counted with multiplicity.

Arithmetic with Complex Numbers

Add, subtract, multiply and divide complex numbers.

Define complex numbers (CCSS.Math.Content.HSN-CN.A.1):

Add, subtract and multiply complex numbers (CCSS.Math.Content.HSN-CN.A.2):

Find conjugates, moduli and quotients of complex numbers (CCSS.Math.Content.HSN-CN.A.3):

Evaluate powers of complex numbers (CCSS.Math.Content.HSN-CN.A.2):

Complex Numbers in Context

Generalize knowledge of polynomials to include complex numbers.

Find complex solutions to quadratic equations (CCSS.Math.Content.HSN-CN.C.7):

Use polynomial identities with complex numbers (CCSS.Math.Content.HSN-CN.C.8):

Reason with the fundamental theorem of algebra (CCSS.Math.Content.HSN-CN.C.9):

Visualize Complex Numbers

Define and plot complex numbers using rectangular or polar coordinates.

Convert between rectangular and polar coordinates (CCSS.Math.Content.HSN-CN.B.4):

Find the distance between two complex numbers (CCSS.Math.Content.HSN-CN.B.6):