JEE Advanced Math — Complex Numbers
Complex numbers for JEE Advanced aspirants — geometry and advanced applications.
📋 Course Learning Outcomes
On successful completion of this course, the learner will be able to:
- Analyze the geometry of complex numbers using rotation, reflection, and similarity transformations [Analyze]
- Derive equations of lines, circles, and conics in complex form and convert between forms [Create]
- Evaluate locus problems involving modulus, argument, and ratio constraints in the Argand plane [Evaluate]
- Apply nth roots of unity to solve equations and to evaluate trigonometric sums [Apply]
- Investigate triangle and polygon geometry — centroid, orthocenter, regularity — using complex coordinates [Analyze]
- Solve JEE Advanced paragraph and integer-type problems involving inequalities of complex numbers [Evaluate]
📚 Chapters
- Algebra and Geometry of Complex Numbers
- Argand Plane and Polar Form
- De Moivre's Theorem and Applications
- nth Roots of a Complex Number
- Roots of Unity and Their Properties
- Locus Problems in the Complex Plane
- Rotation of Vectors
- Lines, Circles and Conics in Complex Form
- Triangle and Polygon Geometry via Complex Numbers
- Inequalities Involving Complex Numbers
- Mixed Advanced Problems
TutorDA LMS