It discusses the need for complex number system and define the complex numbers. It also compares complex numbers with real numbers.

Addition and subtraction of complex numbers can be done arithmetically by adding or subtracting their real parts and separately adding or subtracting their imaginary parts. These operations of complex addition and subtraction can be...

In this video I show you how to find the value of a and b of complex number when you have two complex numbers equal to each other. When two complex numbers are equal to each other the values of a and b must be equal to one...

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...

Multiplying a complex number by another complex number is accomplished using the distributive property to multiply the real and imaginary parts of the first number by the real and imaginary parts of the second number. In this lecture we...

In this video playlist you will learn everything you need to know with complex and imaginary numbers

The concept of imaginary and complex numbers was a powerful innovation that enabled mathematics to progress into previously uncharted territory. Although this concept was not entirely intuitive, extending our number system to include...

👉 Learn about solving rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational equations, one of...

👉 Learn how to solve rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational expressions, one...

👉 Learn how to write the equation of a polynomial when given complex zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The...

In this video playlist I will explain where imaginary and complex numbers come from and how we can use them to help us solve problems. We will also explore the complex property of equality to solve for values of complex numbers.

In this video playlist you will learn everything you need to know with complex and imaginary numbers -7/2i

In this math tutorial I will show you how write a complex number in standard form after simple operations have been performed. You will learn how to find the value of real and imaginary numbers in a complex number and then write it in...

👉 Learn how to write the equation of a polynomial when given complex zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The...

In previous lectures we have seen that quadratic equations that have no solutions when only real values are considered, do have solutions when complex numbers are allowed as input and output values. In this lecture, we check the complex...

In this video, the teacher explains how to solve a quadratic equation with no real solutions using the method of completing the square. They also review complex numbers and common mistakes to avoid when dealing with leading coefficients....

👉 Learn about Descartes' Rule of Signs. Descartes' rule of the sign is used to determine the number of positive and negative real zeros of a polynomial function. Knowing the number of positive and negative real zeros enables also to also...

Fourier series, from the heat equation to sines to cycles.

👉 Learn how to solve rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational expressions, one...

In this video tutorial we will learn how to solve quadratic equations by factoring, completing the square and the quadratic formula. We will first start off by working through factoring quadratic expressions such as factoring out the...

An algorithm for numerically solving certain 2d equations. Even though we described how winding numbers can be used to solve 2d equations at a high level, it's worth pointing out that there are a few details missing for if you wanted to...

An algorithm for solving continuous 2d equations using winding numbers.

An algorithm for solving continuous 2d equations using winding numbers.

👉 Learn how to write the equation of a polynomial when given complex zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The...