Georgia Milestones Algebra II The Complex Number System. Practice it free.

Students perform arithmetic operations with complex numbers and use them 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

  1. Perform arithmetic operations with complex numbers

  2. Use complex numbers in polynomial identities and equations

Standards basis

Georgia Standards of Excellence (state-adopted content standards) — Georgia

How the Georgia Milestones reports it

Georgia Milestones is Georgia’s own statewide assessment system, aligned to Georgia’s state-adopted content standards rather than a shared national test framework. The official page says it measures knowledge and skills in the state-adopted standards for mathematics across grades 3 through high school ([Georgia Department of Education](https://gadoe.org/assessment-accountability/georgia-milestones/)).

Blueprint & weighting

Not published on the official Georgia Milestones overview page reviewed here.

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

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

Expand: (1+6i)(1−6i)=1−6i+6i−36i2=1−36i2(1+6i)(1-6i)=1-6i+6i-36i^{2}=1-36i^{2}. Since i2=−1i^{2}=-1, this is 1+36=37.1+36=37\textsf{.}

Practice playeasy

What is ∣6+8i∣|6 + 8i|?

∣6+8i∣=62+82=100=10|6 + 8i| = \sqrt{6^2 + 8^2} = \sqrt{100} = 10.

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

(3i)2=9i2=9(−1)=−9(3i)^{2} = 9i^{2} = 9(-1) = -9.

Practice playmedium

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

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

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 i3i^{3}?

i3=i2⋅i=(−1)(i)=−ii^{3} = i^{2} \cdot i = (-1)(i) = -i.

Keep practicing

Turn the complex number system into game time.

The Georgia Milestones 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
The same skills on other tests
PARCC
Source and test overview
All Georgia Milestones prepOfficial test source
Reporting categories

More Algebra II domains

Seeing Structure in ExpressionsStudents interpret and rewrite expressions to reveal structure and create equivalent forms.8 QsPractice →Arithmetic with Polynomials and Rational ExpressionsStudents perform arithmetic operations and understand polynomial and rational relationships.8 QsPractice →Creating EquationsStudents create equations and inequalities that model relationships.8 QsPractice →Reasoning with Equations and InequalitiesStudents solve equations and inequalities and analyze systems and algebraic structure.8 QsPractice →Interpreting FunctionsStudents analyze functions and use function notation in context and by representation.8 QsPractice →Building FunctionsStudents build and compare functions that model relationships.8 QsPractice →