MATH1131 > Algebra (Mansfield)

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• (z−α)(z−¯α)=z^2−2Re(α)z+_α_^2
• 2x2 Matrix Inversion
• Angle Between Two Vectors
• Applications
• Cartesian Modification of Complex Numbers
• Cartesian and Parametric Conversions of a Line
• Complex Numbers
• Converting from Cartesian Form to Polar Form
• Converting from Polar Form to Cartesian Form
• Example
• Example_ Does a point belong to a span
• Example_ Express x−2y=1 parametrically
• Example_ Is a point parallel to a plane
• Express sin4θ in terms of powers of cosθ and sinθ
• Express sin^4⁡θ in terms of cosines of multiples of θ
• Geometric Vectors
• Linear Equations and Matrices
• Lines
• Matrices
• Matrix Inversion
• Matrix Transposition & Symmetricity
• Multiplication Checkup
• Normal To the Plane
• Orthogonality
• Planes
• Plotting a complex number on a Cartesian plane
• Point-Normal Form of a Plane
• Polar Form vs Cartesian Form
• Polar Modification of Complex Numbers
• Polar x Cartesian
• Projections
• Properties and Definitions of Matrices
• Roots of z^3+1=0
• Row Operations
• Sets
• Shortest Distance from Point to Plane
• Solubility of a System in Row-Echelon Form
• Solving the square roots of a complex number
• Summary
• The Cartesian Form of a Complex Number
• The Dot Product
• The Polar Form of a Complex Number
• The determinant of a matrix
• The n'th root of a complex number
• Three Points to Parametric_Cartesian
• Vector Uses of Complex Numbers
• Vectors
• Volume of Parallelpiped
• Working with Vectors
• de Moivre's Theorem
• √(−1)=i