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Brian McLogan
Dividing complex numbers by multiplying by the conjugate
In this video tutorial I show you how to divide complex numbers. Since complex numbers have an imaginary part which we cannot divide into other numbers we rewrite the expression by multiplying by i or the conjugate on the denominator or...
Brian McLogan
Multiplication of Complex Numbers
👉 Learn how to multiply radical expressions. In this playlist we will explore multiplying radical expressions and then simplifying. We will explore the square root, cube root as well as the fourth root of numbers and algebraic expressions.
Brian McLogan
What is a complex numbers
Definitions are very important to your understanding of why and how we use mathematical processes. Without understanding what a process or certain terms mean it is very hard to understand how or why to do something. That is why I want to...
Brian McLogan
Complex Zeros of Polynomials | Polynomials | Pre-Calculus
In this video we explore how to determine the complex zeros of a polynomial function by factoring and division. We also will explore the fundamental theorem of algebra, Descartes rule of signs, and the rational zero test.
Brian McLogan
Given the imaginary zeros find the equation of the polynomial
👉 Learn how to write the equation of a polynomial when given imaginary 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...
Brian McLogan
Write the equation of the polynomial given the zeros
👉 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...
Brian McLogan
Given rational function find the vertical asymptote and hole
👉 Learn how to find the removable and non-removable discontinuity of a function. A function is said to be discontinuous at a point when there is a gap in the graph of the function at that point. A discontinuity is said to be removable...
Brian McLogan
How to Evaluate the tangent of double angle using the tangent double-angle formula
👉 Learn how to evaluate the tangent of a half-angle. When given the value of the tangent of an angle, we can evaluate the tangent of half the angle using the tangent half-angle formula. When the value of any other trigonometric function...
Khan Academy
Introduction to Complex Numbers, Imaginary and Complex Numbers, Precalculus
This video continues looking at dividing complex numbers by looking at the conjugate of a complex number. The instructor then uses the conjugate to rationalize the denominator of a rational expression with a complex number in the...
Khan Academy
IIT JEE Complex Numbers (Part 1), Imaginary and Complex Numbers, Precalculus
In this video, a complex number is defined and graphed on the complex plane. Sal also shows how to add, subtract, and multiply two complex numbers. He shows how to divide two complex numbers but runs out of time and continues in the...
Khan Academy
Complex Conjugates, Imaginary and Complex Numbers, Precalculus
Sal discusses the usefulness of the conjugate of the complex number in this video. First, he shows how to add a complex number and its conjugate graphically and algebraically. Then, he shows how to simplify a rational expression with...
Khan Academy
Complex Determinant Example, Imaginary and Complex Numbers, Precalculus
Sal solves a complex determinant problem from the 2010 IIT entrance test. Knowledge of determinants, the exponential form of complex numbers, trigonometric ratios, and algebraic thinking are all utilized here.
Khan Academy
Introduction to I and Imaginary Numbers, Imaginary and Complex Numbers, Precalculus
Students are always fascinated by imaginary numbers. In this video, Sal defines the imaginary unit, i, and shows that it has a cyclic nature when raising i to an exponent.
Khan Academy
Introduction to i and Imaginary Numbers, Imaginary and Complex Numbers, Precalculus
Students are always fascinated by imaginary numbers. In this video, Sal defines the imaginary unit, i, and shows when raising i to an exponent, it has a cyclic nature.
Brightstorm
Introduction to Polar Coordinates - Concept
Learning polar coordinates does not require visiting the North Pole, though explaining igloos is much easier using polar coordinates. The lesson begins with a video explaining how to find coordinates on a spherical plane and how to...
Khan Academy
Khan Academy: Precalculus: Imaginary and Complex Numbers: Basic Complex Analysis
This Khan Academy video lesson provides a concrete way to help students represent and visualize complex numbers. An Argand Diagram, magnitude, modulus, argument, and exponential forms are utilized in the lesson.