Complex numbers
9 videos
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Algebra 2 - What Are Complex Numbers?
An introduction to imaginary and complex numbers, explaining why mathematicians invented i (where i² = -1) and how complex numbers combine real and imaginary parts.
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Algebra 2 - The Imaginary Unit i
An introduction to imaginary numbers, explaining how mathematicians invented 'i' where i² = -1 to solve equations that have no real solutions.
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Algebra 2 - Simplifying Square Roots of Negative Numbers
Learn how to find the square root of negative numbers using the imaginary unit i, and simplify expressions like √-75 step by step.
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Algebra 2 - Powers of i: The Cycle Trick
Learn how to calculate any power of i (imaginary unit) in seconds using the repeating pattern trick and remainders when dividing by 4.
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Algebra 2 - Anatomy of a Complex Number
Learn the standard form of complex numbers (a + bi), how to identify real and imaginary parts, and why all numbers are actually complex numbers.
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Algebra 2 - Plotting on the Complex Plane
Learn how to plot complex numbers on the complex plane by mapping the real part to the horizontal axis and the imaginary part to the vertical axis.
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Algebra 2 - Adding and Subtracting Complex Numbers
Learn how to add and subtract complex numbers by combining real parts with real parts and imaginary parts with imaginary parts, with step-by-step examples.
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Algebra 2 - Multiplying Complex Numbers
Learn to multiply complex numbers using FOIL, then replace i² with -1. Example shows (3+2i)(1-4i) simplified to 11-10i on the complex plane.
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Algebra 2 - Quadratic Equations with Complex Solutions
Learn how to solve quadratic equations with negative discriminants using the quadratic formula, resulting in complex conjugate solutions.