3.5 Algebra and Complex Numbers

Exam content

Past papers can be found here

Link to infinity plus 1 exam paper tutorials, click here

Curriculum content

Algebra

Sum and Product of roots. Video tutorial, web notes.

Completing the square. Video tutorial, notes, practice, answers. Harder examples

The discriminant and its uses. Video 1, video 2 , video 3

Factor and remainder theorem. Video tutorial 1, tutorial 2

Algebraic long division. Factorising cubics. Video 1 . Video 2

Comparing coefficients. Video tutorial

Cubics. Sketching curves

Complex numbers

A history for those interested

a. Introducing Complex Numbers

b. Working with Complex Numbers

c. Complex Conjugates

Complex numbers in modulus and argument form, and argand diagrams

a. Introducing the Argand Diagram

b. Introducing Modulus-Argument Form

c. Multiply and Divide in Modulus-Argument Form

d. Loci with Argand Diagrams

De Moivre's Theorem and Polar form

a. De Moivre's Theorem

b. z = re^(iθ)