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"Complex" numbers share many properties with the real numbers. In fact, complex numbers include all the real numbers, so you know lots of them already. Such an overachiever.

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Complex Numbers Warmup
Arithmetic
Complex Conjugates
Argand Plane
Factoring Polynomials
Problem Solving

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Complex Numbers - Argand Plane

Suppose that we have two complex numbers \(z_1 = 3 - 2i\) and \(z_2 = 4 - 3i\). In what quadrant is this complex number \(z_1z_2\) located?

Quadrant I Quadrant II Quadrant III Quadrant IV

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by Brilliant Staff

What is the shape of graph of the equation \(\left|z\right| = 4\) in the complex plane?

Square Line Parabola Circle

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by Brilliant Staff

In \( \text{units}^2\), what is the area of the rectangle formed by the vertices \(2 + 3i, 4 + 2i, -i\), and \(2 - 2i\)?

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by Brilliant Staff

Suppose the function \(f(z)\) takes the complex number \(z\) and rotates it 90 degrees counterclockwise around the origin.

Which function represents this transformation?

\[f(z) = iz\] \[f(z) = \bar{z}\] \[f(z) = -z\] \[f(z) = z^2\]

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by Brilliant Staff

For a complex number \(z\), on which part of the Argand plane does \(\text{Re}(z) + \text{Im}(iz)\) sit?

Origin First Quadrant Imaginary axis Real axis

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by Brilliant Staff

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Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

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Complex Numbers

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

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Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

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Concept Quizzes

Challenge Quizzes

Complex Numbers - Argand Plane

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

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Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

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Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

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Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.