Complex Numbers & Polynomials- Both Basic & Advanced

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Learn the fundamentals of polynomials & complex numbers for absolute beginners (Polar form, Euler's form, De Moivre's)

What you'll learn
Conceptual understanding of why we need complex numbers
Solving a polynomial equation
Undertake Operations of complex numbers like Addition, Multiplication & Division
Find zeros, roots and factors of a polynomial function
Graphically understand the dynamics of polynomial equation
Complex Conjugates
Understand the Polar form of a complex number
Euler's Form
De Moivre's Theorem
Roots of Complex Numbers
Cube Roots of Unity
Requirements
This course is for beginners. Basic knowledge equivalent of class 7 is expected. Basic knowledge of trigonometry will be useful.
The students will find it easier if they are familiar with basic algebra.
Description
Just like everything in this universe is made up of atoms which in turn is made up of sub-atomic structures like electrons, protons and neutrons, everything in the mathematical universe is made up of complex numbers. In that sense, complex numbers are the most fundamental elements of the mathematical universe. Everything we know of numbers since elementary school also applies to complex numbers. But everything we know of complex numbers doesn't apply to real numbers. This is because, complex numbers consists of imaginary numbers (that we do not know of) in addition to real numbers (that we know everything of). So, learning complex numbers is fun. We revisit everything we know of and generalize the result and understanding so that it applies all the numbers i.e. real and imaginary.
Any given function has at least a solution. This is a mathematical way of saying that the graph of the function when plotted cuts the X-axis at least once. A simple way to put it is 'the number of times a function cuts the X-axis, the same number of X will satisfy the given equation. When a given X satisfies a given equation, it is the root of the given equation. But it turns out that there are functions which do not seem to cut X-axis for any value of X. So for those functions we do not have a root or solution. It was insulting for the mathematicians to know that a function may not have a solution which is why they invented complex numbers. Now with the introduction of complex numbers, even those functions which had no solution, seem to have a solution. But this solution is called a complex solution because it is in the form of a complex numbers. Although this solution is imaginary (and therefore not real), this is actually contributing to newer real avenues of discovery and research. After the completion of the course, you will see and do problems involving how an imaginary number raised to a power of another imaginary number also might lead to a real number.
The above paragraph is a simple yet effective way of knowing what to expect out of this course. If you want to know the fact of this matter, please enroll in the course where we have covered everything there is to know on the topic.
Who this course is for
Beginners high school students
high school students
Competitive exams aspirants
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