Complex Numbers and Quadratic Equations — Class 11 CBSE Mathematics revision notes
A 3-page visual revision sheet for Complex Numbers and Quadratic Equations, written for Class 11 CBSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
What this Complex Numbers and Quadratic Equations sheet covers
- Why i exists
- Algebra of complex numbers
- addition: real to real, imaginary to imaginary
- subtraction: the same way
- multiplication: expand like binomials, then replace i^2 with -1
- Conjugate and modulus
- conjugate of z=a+bi: flip the sign of the imaginary part
- a number times its own conjugate is always real
- modulus: distance of z from the origin
- Division, by clearing i from the denominator
- multiply by the conjugate of the denominator
- Powers of i cycle every 4
- n leaves remainder 1
- n leaves remainder 2
- n leaves remainder 3
- n leaves remainder 0
- Square root of a negative real number
- Polar form, reading z off the Argand plane
- Finding the argument
- A quadratic equation with complex roots
- Nature of the roots of ax²+bx+c=0
- The quadratic formula, restated for any real a, b, c
- the two roots
- sum of the roots
- product of the roots
- Symbols
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Complex Numbers and Quadratic Equations the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.