Transformations using a Matrix What is a transformation matrix? A transformation matrix is used to determine the coordinates of an image from the transformation of an object reflections, rotations,...
Inverse of a Matrix What is an inverse of a matrix? The determinant can be used to find out if a matrix is invertible or not: If , then is invertible If , then is singular and does not have an in...
Determinant of a 2x2 Matrix What is a determinant? The determinant is a numerical value (positive or negative) calculated from the elements in a matrix and is used to find the inverse of a matrix Y...
Introduction to Matrices Matrices are a useful way to represent and manipulate data in order to model situations. The elements in a matrix can represent data, equations or systems and have many rea...
Roots of Complex Numbers How do I find the square root of a complex number? The square roots of a complex number will themselves be complex: i.e. if We can then square and equate it to the original...
Multiple Angle Formulae de Moivre’s theorem can be applied to prove identities such as . This allows expressions involving multiple angles to be written as a polynomial function of a single trig fu...
De Moivre's Theorem What is de Moivre’s Theorem? de Moivre’s theorem can be used to find powers of complex numbers It states that for Where z ≠ 0 r is the modulus, |z|, r ∈ ℝ+ θ is the argument, a...
Exponential Form You now know how to do lots of operations with complex numbers: add, subtract, multiply, divide, raise to a power and even square root. The last operation to learn is raising the n...
Inequalities & Regions in Argand Diagrams How do I sketch inequalities such asor on an Argand diagram? The inequality is satisfied by all complex numbers, , with a real part less than 2 On an ...
