Exercise 1.1 — Question 1 Key Concepts Reviewed Definition of a Complex Number (M-11-A-01) A complex number is any numb

Exercise 1.1 — Question 2 This exercise covers basic operations on complex numbers, equality of complex numbers, and eva

Exercise 1.1 — Question 3 This question practices basic operations on complex numbers and applying the equality conditio

Exercise 1.1 — Question 4 Powers of The imaginary unit is defined as , so . The powers of follow a cyclic pattern wit

Exercise 1.1 — Question 5 Question Simplify the following powers of : (i)    (ii)    (iii)  

Exercise 1.1 — Question 6 Powers of Recall that , so the powers of cycle with period 4: For any integer , divide by 4

Exercise 1.1 — Question 7 Problem Evaluate the following powers of : (i)   (ii)   (iii)   (iv) --- Ke

Exercise 1.2 — Question 1 Basic Operations on Complex Numbers For two complex numbers and where : Addition Subtraction

Exercise 1.2 — Question 2 This exercise covers basic operations on complex numbers, including multiplication by and con

Exercise 1.2 — Question 3 This question covers basic operations on complex numbers, properties of the complex conjugate,

Exercise 1.2 — Question 4 This exercise covers basic operations on complex numbers, properties of the complex conjugate,

Exercise 1.2 — Question 5 Key Concepts Covered This question covers basic operations on complex numbers (SLO M-11-A-04),

Exercise 1.2 — Question 6 This exercise covers basic operations on complex numbers, properties of the complex conjugate,

Exercise 1.2 — Question 7 This question covers basic operations on complex numbers, the complex conjugate, and the modul

Exercise 1.2 — Question 8 This question covers basic operations on complex numbers, the complex conjugate, and propertie

Exercise 1.2 — Question 9 Key Concepts Reviewed This question applies three core ideas about complex numbers: 1. Basic o

Exercise 1.2 — Question 10 Problem Statement If , find and . Also state the condition for to be purely real in terms o

Exercise 1.3 — Question 1 This exercise covers two key skills: 1. Factorizing expressions of the form into linear facto

Exercise 1.3 — Question 2 Topic: Simultaneous Linear Equations with Complex Coefficients SLO: Solve simultaneous linear

Exercise 1.3 — Question 3 Problem Factorize the following into linear factors: (i) (ii) (iii) --- Key Concept: Factor

Exercise 1.3 — Question 4 This question covers factorization of polynomials over (SLO M-11-A-08) and solving quadratic

Exercise 1.4 — Q1: Simultaneous Linear Equations with Complex Coefficients Key Method To solve simultaneous linear equat

Exercise 1.4 — Question 2: Simultaneous Linear Equations with Complex Coefficients This exercise covers solving systems

Exercise 1.4 — Question 3 Problem Solve the following simultaneous linear equations with complex coefficients: Solution

Exercise 1.4 — Question 4 This exercise covers the equality of complex numbers, basic algebraic operations, and solving

Exercise 1.4 — Question 5 Polar Representation of Complex Numbers This question involves converting complex numbers to p

Exercise 1.4 — Question 6 Topic: Operations with Complex Numbers in Polar Form This question applies polar (trigonometri

Exercise 1.4 — Question 7 Problem Solve the following simultaneous linear equations with complex coefficients: Method: E

Exercise 1.4 — Question 8 Topic: Operations with Complex Numbers in Polar Form This question involves applying operation

Exercise 1.4 — Question 9 Topic: Operations with Complex Numbers in Polar Form This question applies the polar (trigonom

Exercise 1.4 — Question 10 Polar Representation of Complex Numbers A complex number can be written in polar (trigonomet