Common Core · High school
HSN-CN.B.4
High school — 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.
A note on this mapping: HSN-CN.B.4 is a (+) standard — beyond the college- and career-ready threshold, i.e. precalculus rather than Algebra II.
The skill that covers it
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.