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Complex Numbers: Geometrical Approach

Learning tasks
                      
Lesson Summary
Text book
Exercises Correction
A) Complex Plane
    1) Reading the Affix of a PointEx 1 Ex 2 Ex 3 Ex 4
    2) Conjecturing the Nature of a FigureEx 5 Ex 6 Ex 7
B) Modulus and Argument
    3) Calculating the Modulus of a Complex NumberEx 8 Ex 9 Ex 10 Ex 11
    4) Calculating the Argument of a Complex NumberEx 12 Ex 13 Ex 14
C) Unit Modulus Complex Numbers and the Imaginary Exponential
    5) Finding the Affix of a Point on the Unit CircleEx 15 Ex 16 Ex 17 Ex 18
    6) Evaluating Complex ExponentialsEx 19 Ex 20 Ex 21 Ex 22
    7) Applying the Properties of ExponentsEx 23 Ex 24 Ex 25 Ex 26 Ex 27 Ex 28
D) Polar and Euler's Forms
    8) Converting from Polar to Standard FormEx 29 Ex 30 Ex 31 Ex 32
    9) Converting from Standard to Polar FormEx 33 Ex 34 Ex 35
    10) Converting from Polar to Euler's FormEx 36 Ex 37 Ex 38
E) De Moivre's Theorem
    11) Applying De Moivre's TheoremEx 39 Ex 40 Ex 41
F) Properties of Modulus and Argument
    12) Proving the Properties of the ModulusEx 42 Ex 43 Ex 44
    13) Proving the Properties of the ArgumentEx 45 Ex 46 Ex 47
G) Geometry in the Coordinate Plane
    14) Visualizing Fundamental TransformationsEx 48 Ex 49 Ex 50 Ex 51
    15) Calculating Distances, Midpoints, and AnglesEx 52 Ex 53 Ex 54 Ex 55
    16) Proving the Nature of Geometric FiguresEx 56 Ex 57 Ex 58
H) Geometric Loci in the Complex Plane
    17) Plotting LinesEx 59 Ex 60 Ex 61 Ex 62
    18) Plotting Rays in the Complex PlaneEx 63 Ex 64 Ex 65
    19) Identifying Loci from Modulus EquationsEx 66 Ex 67 Ex 68 Ex 69
I) Roots of Complex Numbers
    20) Finding the n-th Roots of a Complex NumberEx 70 Ex 71 Ex 72 Ex 73 Ex 74