We've learned a bit about quantum mechanics from a strictly conceptual and qualitative standpoint. But now it's time to dig a little deeper. Quantum mechanics is mathematics, so if we want to understand it on a fundamental level, we have...

We all know what numbers are 1, 2, 3, 4, 5, …. Including negative numbers -1, -2, -3, -4, -5, ... But did you know that mathematicians classify numbers into different types… into a number system. Let’s start at the top with real numbers....

In this video, the teacher explains how to graph cube root functions by using transformations. They review inverse functions and how they reflect over the line y = x. They also discuss the domain and range of cube root functions and...

👉 Learn how to add or subtract two functions. Given two functions, say f(x) and g(x), to add (f+g)(x) or f(x) + g(x) or to subtract (f - g)(x) or f(x) - g(x) the two functions we use the method of adding/subtracting algebraic expressions...

Zach Star demonstrates a surprising topological proof - you can always cut three objects in half with a single plane

It explains the derivation of formula to obtain the distance between two points in space. It also provides some solved examples on computing the distance between two points.

In this video series I show you how to determine if a relation is a linear relation. A linear relation is a relation where their are variables do not have negative or fractional, or exponents other than one. Variables must not be in the...

This nugget explains the proof of the Factor theorem. It includes problems and their solutions based on the theorem.

In this lesson, we explored the complex number system, which extends the real number system. We learned that complex numbers consist of a real part and an imaginary part, represented as a + bi, where a and b are real numbers and i is the...

It explains how to add and subtract two complex numbers. It also shows the graphical representation of sum and difference of two complex numbers.

👉 Learn how to find the domain of rational functions. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function, the denominator cannot be zero. Thus, to find the domain...

👉 Learn how to classify numbers. We will classify numbers as real, imaginary, rational, and irrational.

👉 Learn how to classify numbers. We will classify numbers as real, imaginary, rational, and irrational.

👉 Learn how to find the domain of rational functions. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function, the denominator cannot be zero. Thus, to find the domain...

This lesson covers the commutative property, associative property, and distributive property, and provides examples of how these properties apply to complex numbers. By extending their knowledge of real number properties, students will...

👉Learn how to solve quadratic functions. Quadratic equations are equations whose highest power in the variable(s) is 2. They are of the form y = ax^2 + bx + c. There are various techniques which can be applied in solving quadratic...

In this video series I will show you how to combine complex number by either subtracting or adding them together. Complex numbers have real and imaginary components. When combining complex numbers we can only add the real to the imaginary.

👉 Learn how to find the domain of rational functions with radicals in both the numerator and the denominator. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function,...

In this video lesson, you will learn how to determine whether the solutions of a quadratic equation are real or imaginary by calculating the value of the equation's discriminant. The discriminant, which is found under the square root...

👉 You will learn how to add and subtract integers. We will work through adding and subtracting two integers up to multiple integers. We can look at adding and subtracting integers by looking at there values on a number line where there...

👉 Learn how to find the zeroes of a polynomial equation/expression involving the sum/difference of two cubes. Given a polynomial having the sum of two cubes, the polynomial can be factored as follows: a^3 + b^3 = (a + b)(a^2 - ab + b^2)....

In this video tutorial I will show you how to add and subtract complex numbers. When combining complex numbers it is important for us to understand that we must have like terms. We then add and subtract in either the horizontal or...

👉Learn how to solve quadratic functions. Quadratic equations are equations whose highest power in the variable(s) is 2. They are of the form y = ax^2 + bx + c. There are various techniques which can be applied in solving quadratic...

Dividing complex numbers can be more complicated than multiplying complex numbers since when the result is a fraction, in order to write that fraction as a complex number in standard form, it must be separated into a real part plus an...