PARCC Algebra II The Complex Number System. Practice it free.

Students perform arithmetic operations with complex numbers and use complex numbers in polynomial identities and equations. This Algebra II reporting domain maps to 3 practice skills and 8 representative questions from the playable bank.

Algebra II3 mapped skills

What the test measures

The Complex Number System skills

Perform arithmetic operations with complex numbers
Use complex numbers in polynomial identities and equations

Standards basis

Common Core State Standards for Mathematics (CCSS-M) / PARCC Model Content Frameworks — national

How the PARCC reports it

PARCC was a multistate assessment system built around the Common Core-era PARCC mathematics model content frameworks rather than a separate proprietary standards set. Its math structure is organized by grade/course and aligned to CCSS-M content categories and model content frameworks.

Blueprint & weighting

No single published PARCC weighting table was located in the accessible sources used here.

Official sources

PARCC Assessment
Common Core State Standards Initiative

Practice by skill

Topics mapped to this domain

Multiplying and squaring complex numbers (ACT)

Grade 1110 questions

Complex number operations

Grade 1117 questions

Rewriting complex numbers

Grade 1110 questions

Try it now

8 free questions · 0/0 correct

Practice playmedium

What is the value of $(4+i)(3+2i)$ ?

Expand: $(4+i)(3+2i)=12+8i+3i+2i^{2}$ . Since $i^{2}=-1$ , this is $12+11i-2=10+11i\textsf{.}$

Practice playeasy

What is $|5 + 12i|$ ?

$|5 + 12i| = \sqrt{5^2 + 12^2} = \sqrt{169} = 13$ .

Practice playmedium

Given $i = \sqrt{-1}$ , what is $\sqrt{49} - \sqrt{-16}$ ?

$\sqrt{49} = 7$ and $\sqrt{-16} = 4i$ . So $\sqrt{49} - \sqrt{-16} = 7 - 4i$ .

Practice playmedium

$(1+6i)(1-6i)$ is equal to which of the following?

Expand: $(1+6i)(1-6i)=1-6i+6i-36i^{2}=1-36i^{2}$ . Since $i^{2}=-1$ , this is $1+36=37\textsf{.}$

Practice playeasy

What is $(2i)^2$ ?

$(2i)^2 = 4i^2 = 4(-1) = -4$ .

Practice playmedium

Given $i = \sqrt{-1}$ , what is $\sqrt{121} - \sqrt{-9}$ ?

$\sqrt{121} = 11$ and $\sqrt{-9} = 3i$ . So $\sqrt{121} - \sqrt{-9} = 11 - 3i$ .

Practice playmedium

What is $(3+2i)^{2}$ ?

Expand: $(3+2i)^{2}=9+12i+4i^{2}$ . Since $i^{2}=-1$ , this is $9+12i-4=5+12i\textsf{.}$

Practice playeasy

What is $i^{6}$ ?

$i^{6} = (i^{2})^{3} = (-1)^{3} = -1$ .

Keep practicing

Turn the complex number system into game time.

The PARCC placement starts with this test's real coverage map and finds the right difficulty.

Batting Cage game cover

Batting CagePlay →

Blossom Leap game cover

Blossom LeapPlay →

Buzzer Beater game cover

Buzzer BeaterPlay →

Minecart Junction game cover

Minecart JunctionPlay →

Related Common Core standards

HSN.CN.A.2 HSN.CN.A.1

The same skills on other tests

Georgia Milestones

Source and test overview

All PARCC prep Official test source

Reporting categories

More Algebra II domains

Seeing Structure in ExpressionsStudents interpret the structure of expressions and write expressions in equivalent forms to solve problems.8 QsPractice →Arithmetic with Polynomials and Rational ExpressionsStudents perform arithmetic operations on polynomials and rational expressions.8 QsPractice →Creating EquationsStudents create equations and inequalities to represent relationships.8 QsPractice →Reasoning with Equations and InequalitiesStudents solve equations and inequalities and reason with them.8 QsPractice →Interpreting FunctionsStudents interpret and analyze functions in context and by multiple representations.8 QsPractice →Building FunctionsStudents build and compare functions and use recursive and explicit expressions.8 QsPractice →