NJSLA Algebra II Complex Number System. Practice it free.

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 IIN-CN3 mapped skills
What the test measures

Complex Number System skills

  1. N.CN.A.1-3 Complex number arithmetic and powers of i

  2. N.CN.B.4-5 Use complex numbers in polynomial identities and equations

Standards basis

New Jersey Student Learning Standards for Mathematics (NJSLS-M), aligned to Common Core State Standards for Mathematics (CCSS-M) — New Jersey

How the NJSLA reports it

NJSLA math is built on the New Jersey Student Learning Standards for Mathematics, which closely follow the Common Core domain structure and progressions. The assessment is organized by grade-level and end-of-course reporting aligned to those standards rather than by a separate proprietary framework.

Blueprint & weighting

NJDOE publishes statewide assessment administration information and grade/course coverage, but no official public math-domain weighting blueprint was located in the retrieved primary materials.

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 (3+2i)2(3+2i)^{2}?

Expand: (3+2i)2=9+12i+4i2(3+2i)^{2}=9+12i+4i^{2}. Since i2=−1i^{2}=-1, this is 9+12i−4=5+12i.9+12i-4=5+12i\textsf{.}

Practice playeasy

What is i6i^{6}?

i6=(i2)3=(−1)3=−1i^{6} = (i^{2})^{3} = (-1)^{3} = -1.

Practice playeasy

Given i=−1i = \sqrt{-1}, what is 100+−49\sqrt{100} + \sqrt{-49}?

100=10\sqrt{100} = 10 and −49=7i\sqrt{-49} = 7i. So 100+−49=10+7i\sqrt{100} + \sqrt{-49} = 10 + 7i.

Practice playmedium

Simplify (4−i)2(4-i)^{2}.

Expand: (4−i)2=16−8i+i2(4-i)^{2}=16-8i+i^{2}. Since i2=−1i^{2}=-1, this is 16−8i−1=15−8i.16-8i-1=15-8i\textsf{.}

Practice playeasy

What is ∣8+15i∣|8 + 15i|?

∣8+15i∣=82+152=289=17|8 + 15i| = \sqrt{8^2 + 15^2} = \sqrt{289} = 17.

Practice playmedium

Given i=−1i = \sqrt{-1}, what is 36+−81\sqrt{36} + \sqrt{-81}?

36=6\sqrt{36} = 6 and −81=9i\sqrt{-81} = 9i. So 36+−81=6+9i\sqrt{36} + \sqrt{-81} = 6 + 9i.

Practice playhard

Multiply: (5−3i)(−2+i)(5-3i)(-2+i).

Expand: (5−3i)(−2+i)=−10+5i+6i−3i2(5-3i)(-2+i)=-10+5i+6i-3i^{2}. Since i2=−1i^{2}=-1, this is −10+11i+3=−7+11i.-10+11i+3=-7+11i\textsf{.}

Practice playeasy

What is (4i)2(4i)^2?

(4i)2=16i2=16(−1)=−16(4i)^2 = 16i^2 = 16(-1) = -16.

Keep practicing

Turn complex number system into game time.

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

Batting Cage game coverBatting CagePlay →Blossom Leap game coverBlossom LeapPlay →Buzzer Beater game coverBuzzer BeaterPlay →Minecart Junction game coverMinecart JunctionPlay →
Related Common Core standards
HSN.CN.A.2HSN.CN.A.1
Source and test overview
All NJSLA prepOfficial test source
Reporting categories

More Algebra II domains

The Real Number SystemExtend the properties of exponents to rational exponents and use properties of radicals and integer exponents.8 QsPractice →QuantitiesReason quantitatively and use units to solve problems.8 QsPractice →Seeing Structure in ExpressionsInterpret the structure of expressions and write expressions in equivalent forms to solve problems.8 QsPractice →Arithmetic with Polynomials and Rational ExpressionsPerform arithmetic operations on polynomials and rational expressions.8 QsPractice →Creating EquationsCreate equations that describe numbers or relationships.8 QsPractice →Reasoning with Equations and InequalitiesUnderstand solving equations as a process of reasoning and solve equations and inequalities.8 QsPractice →