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# Precalculus

What are the imaginary numbers?: Complex numbersWhat are the complex numbers?: Complex numbersThe complex plane: Complex numbersAdding and subtracting complex numbers: Complex numbersDistance and midpoint of complex numbers: Complex numbers

Multiplying complex numbers: Complex numbersComplex conjugates and dividing complex numbers: Complex numbersIdentities with complex numbers: Complex numbersAbsolute value and angle of complex numbers: Complex numbersPolar form of complex numbers: Complex numbersMultiplying and dividing complex numbers in polar form: Complex numbers

Introduction to matrices: MatricesRepresenting linear systems of equations with augmented matrices: MatricesElementary matrix row operations: MatricesRow-echelon form and Gaussian elimination: MatricesAdding and subtracting matrices: MatricesMultiplying matrices by scalars: MatricesProperties of matrix addition & scalar multiplication: MatricesMultiplying matrices by matrices: Matrices

Properties of matrix multiplication: MatricesMatrices as transformations: MatricesThe determinant of a 2x2 matrix: MatricesIntroduction to matrix inverses: MatricesFinding the inverse of a matrix using its determinant: MatricesPractice finding the inverses of 2x2 matrices: MatricesSolving equations with inverse matrices: MatricesModel real-world situations with matrices: Matrices

Introduction to conic sections: Conic sectionsThe features of a circle: Conic sectionsStandard equation of a circle: Conic sectionsExpanded equation of a circle: Conic sectionsCenter and radii of an ellipse: Conic sectionsFoci of an ellipse: Conic sections

Focus and directrix of a parabola: Conic sectionsIntroduction to hyperbolas: Conic sectionsFoci of a hyperbola: Conic sectionsHyperbolas not centered at the origin: Conic sectionsIdentifying conic sections from their equations: Conic sectionsChallenging conic section problems (IIT JEE): Conic sections

Basic probability: Probability and combinatoricsVenn diagrams and the addition rule: Probability and combinatoricsCompound probability of independent events using diagrams: Probability and combinatoricsCompound probability of independent events using the multiplication rule: Probability and combinatorics

Test your knowledge of the skills in this course. Have a test coming up? The Course challenge can help you understand what you need to review.

## Get StartedWhat are the imaginary numbers?

Learn about the imaginary unit i (which is the square root of -1) and about imaginary numbers like 3i (which is the square root of -9).

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