Common Core · High school

HSN-CN.B.6

High school — 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.

A note on this mapping: HSN-CN.B.6 is a (+) standard — beyond the college- and career-ready threshold, i.e. precalculus rather than Algebra II.

The skill that covers it

The Complex Plane & Polar FormSee a complex number as a point and an arrow: plot a + bi, read its modulus as a distance and its argument as an angle, convert between rectangular and polar form, multiply and divide in polar form, raise to a power with De Moivre, and find every nth root.Read the lesson →

What a student should be able to do

Plot a complex number, and find the modulus and argument of $a +$ bi.
Convert between rectangular form $a +$ bi and polar form r(cos θ $+$ i sin θ), and between polar and rectangular coordinates of a point.
Multiply and divide complex numbers in polar form, and use De Moivre's theorem to raise one to a power.
Find the nth roots of a complex number and describe where they sit on the plane.

Every Common Core code covered by Math Vale