Is Goblins free for teachers?

Yes. Goblins offers a generous free tier that includes 1 live feedback assignment per week, insights on student mastery and replays, and the ability to upload your own content. The Max plan adds unlimited assignments, superadaptive mode, grade exports, standards growth reports, and SSO/LMS integration, with per-student pricing for schools and districts.

How does Goblins work?

Three simple steps: (1) Share an assignment from thousands of standards-aligned topics using a share code. (2) Students speak and draw their thinking naturally, and Goblins responds with Socratic questioning that sounds just like their teacher. (3) Teachers get real-time formative insights showing what students struggle with and suggestions to inform instruction.

Does Goblins prevent cheating?

Yes. Goblins uses a purpose-trained AI model that evaluates cheating signals in real time. It can detect when students are copying answers, using external tools inappropriately, or not genuinely working through problems. Copy-pasting answers is also blocked.

Can I use my own voice with Goblins?

Yes. Teachers can record their voice and take a selfie to create a custom 3D avatar in about 30 seconds. Students then hear help in their own teacher's voice and see a familiar face, making the experience more personal and effective.

What math levels does Goblins cover?

Goblins covers math from Grade 5 through AP Calculus, including thousands of standards-aligned topics. Teachers can also upload their own content for custom assignments at any level.

Is Goblins FERPA compliant?

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Does Goblins support English Language Learners?

Yes. Goblins supports 30+ languages so teachers don't have to translate every worksheet. It is especially helpful for ELL students who need accessible math instruction in their native language.

What grade level is N-CN taught?

This standard is part of the N-CN curriculum in Alaska Mathematics Standards.

N-CN: The Complex Number System

The Complex Number System

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The Complex Number System introduces i as the square root of -1 and extends arithmetic to complex numbers in standard form. Operations on complex numbers, including multiplication, conjugates, and moduli, are practiced and connected to polynomial factoring. The Fundamental Theorem of Algebra establishes that every polynomial has roots in the complex number system.

N-CN.1Know there is a complex number i such that i^2 = –1, and every complex number has the form a + bi with a and b real.N-CN.2Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.N-CN.3(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.N-CN.4(+) 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.N-CN.5(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (1 – root 3i)3 = 8 because (1 – root 3i) has modulus 2 and argument 120°.N-CN.6(+) 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.N-CN.7Solve quadratic equations with real coefficients that have complex solutions.N-CN.8(+) Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).N-CN.9(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Example Problems

Simplify:

i^2

Simplify:

i^{6}

Divide the following complex numbers.

\frac{5 + 5i}{1 + 2i}

x = 12 + 9i

What is the imaginary part of x?

Consider the complex number:

z = i

What is

z^{11}

?

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