Complex numbers specimen questions (mixed exam boards)
Complex numbers In this tutorial, we solve problems from different exam boards involving complex numbers. The idea is to give you a more rounded approach to solving different topic problems. Edexcel A-Level Further Maths Specimen Paper 1 Q3 (Core Pure 1) 9 MARKS IB Maths AA HL Specimen Paper 1 (Section B) a) 5MARKS b) […]
Solving hyperbolic equations using hyperbolic identities
Osborn’s rule
The locus of a point moving in a circle
nth roots of a complex number
Expressing sinnθ and cosnθ in terms of sin(kθ) and cos(kθ)
Expressing sin(nθ) and cos(nθ) in terms of sinθ and cosθ
De Moivre’s theorem
Multiplication and division rules for mod and argument of two complex numbers
Exponential Form (Euler’s relation)
Method of differences
Modulus inequalities fractional type
Fractional inequalities
Matrix proofs
Divisibility and multiple test proofs
Proof for other series
Proof of the sum of the series ∑r³
Proof of the sum of the series ∑r²
Proof of the sum of the series ∑r
Using known formulae to sum more complex series
Sum of the cubes of the first n natural numbers ∑r3
Sum of the squares of the first n natural numbers ∑r2
Combinations of transformations
How well do you know your transformations?
Linear transformations – enlargement
Linear transformations – reflections
Linear transformations – rotations
Solving simultaneous linear equations in 2 unknowns
Sum of the first n natural numbers ∑r and the results for ∑a and ∑(ar+b)
Identity and Inverse of a 2×2 matrix
Matrix multiplication
Addition and subtraction and multiplying a matrix by a scalar
Introduction and dimension of a matrix
Solving problems with complex numbers
Modulus and argument of a complex number
Argand diagrams
Division of a complex number by a complex number
Complex conjugates
Addition, subtraction and multiplying complex numbers and simplifying powers of i
Real and imaginary numbers
Closest point to a line and shortest distance from the origin
Intersecting and skew lines
Parallel lines
Angle between two lines
Vector equation of a line
Perpendicular vectors
Scalar product
Volume of revolution about the x-axis
Integrals involving partial fractions
Infinite integrals
In this tutorial I show you how to handle integrals where a limit is infinite as in the example below. Example: