Complex Numbers

This math unit progresses from basic to advanced concepts involving complex numbers. Initially, students focus on rewriting and simplifying complex numbers, starting with square roots containing negative radicands. They practice expressing these roots in terms of complex numbers and simplifying radicals. As the unit advances, students engage with operations on the complex plane, such as subtraction and division of complex numbers, specifically focusing on imaginary parts. To deepen understanding, they also simplify and evaluate powers of the imaginary unit, \(i\). Later, the unit moves toward geometric interpretations and transformations of complex numbers, including calculating absolute values and converting between polar and rectangular forms in both radians and degrees. They apply trigonometric functions and Euler’s formula, essential for converting complex numbers' exponential form into rectangular form. These cumulative skills build a comprehensive understanding of complex number manipulation, encompassing algebraic operations and geometric interpretations.

Skills you will learn include:

Foundational Units

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Learning through Game Play

At Mobius we have lots of great (and free) resources to help you learn math. To keep kids engaged, there’s nothing better than a math-powered video game! Try out a Mobius game mapped to Complex Numbers.

This math topic focuses on the skill of rewriting square roots of negative numbers as complex numbers, particularly using...

This math topic focuses on complex numbers, specifically how to rewrite roots of negative numbers as complex numbers and...

This math topic focuses on advanced manipulation of complex numbers, specifically the skill of rewriting square roots that...

This topic focuses on adding and subtracting complex numbers, a fundamental skill within the larger area of complex number...

This math topic focuses on practicing the multiplication of imaginary numbers, specifically those parts of complex numbers...

This math topic focuses on practicing complex numbers, specifically rewriting roots as complex numbers and simplifying radicals....

This math topic focuses on practicing the multiplication of complex numbers and simplifying the results. The problems require...

This math topic focuses on practicing addition in the complex plane, a component of complex numbers. The problems present...

This math topic focuses on practicing subtraction of complex numbers on the complex plane. Each problem requires determining...

This math topic focuses on finding the complex conjugates of given complex numbers. It deals with the concept of changing...

This math topic focuses on finding the complex conjugates of points on the complex plane. It includes various problems that...

This math topic focuses on dividing complex numbers, specifically emphasizing cases where only the imaginary parts are involved....

This math topic focuses on practicing the division of complex numbers, enhancing skills in simplifying expressions that involve...

This math topic focuses on simplifying the powers of the imaginary unit \( i \). The problems involve calculating the result...

This math topic focuses on simplifying powers of the imaginary unit \( i \). Practicing these problems helps build understanding...

This math topic focuses on converting angles from degrees to radians. It is designed for learners at level 1, within the...

This math topic emphasizes the conversion of angles measured in radians into degrees. Each problem supplies an angle in radians...

This math topic helps students practice finding the absolute value of a point on the complex plane. Students are given different...

This topic focuses on practicing advanced trigonometry skills, specifically solving for side lengths from diagrams, as part...

This math topic focuses on converting complex numbers from polar (modulus and argument in degrees) to rectangular form. Each...

This math topic focuses on converting complex numbers from polar form (modulus and argument in radians) to rectangular form....

This math topic focuses on converting complex numbers from rectangular form to polar form, specifically finding the modulus...

This math topic focuses on converting complex numbers from rectangular form to polar form, specifically calculating the modulus...

This math topic focuses on converting complex numbers from rectangular form to polar form in degrees. Learners are presented...

This math topic focuses on converting complex numbers from polar form (given in degrees) to rectangular form. Each question...

This math topic focuses on converting complex numbers from rectangular form to polar form using radians. Each question provides...

This math topic focuses on converting complex numbers from polar form (using radians) to rectangular form. It includes problems...

This math topic focuses on converting complex numbers from rectangular form to exponential form using radians. Students practice...

This math topic focuses on converting complex numbers from polar form to exponential form using radians. It includes multiple...

This topic focuses on practicing the conversion of complex numbers from exponential form (expressed in radians) to rectangular...

This math topic focuses on converting complex numbers from exponential form to polar form, specifically using radians. It...

This math topic focuses on identifying and interpreting points in the complex plane, relevant to the broader unit on complex...

This math topic involves calculating the distance between two points on the complex plane, under the broader theme of complex...

This math topic focuses on applying the Pythagorean Theorem to find the length of the hypotenuse of a right triangle, with...