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Finding All Complex Roots of z^7 + 50 = 0

An educational slide presenting the problem of finding all complex roots for the equation z^7+50=0. The layout is structured into three sections: the Problem Statement, which defines the algebraic equation over the field of complex numbers C; the Objective, which invokes the Fundamental Theorem of Algebra to establish the existence of exactly seven roots; and Step 1, which begins the solution process by rearranging the equation to z^7=−50 and defining the modulus of a complex number. Timecode: 00:00 Problem Statement: z^7 + 50 = 0 00:29 Step 1: Rewrite in Exponential Form 01:18 Step 2: Apply the Root Formula 01:52 Step 3: Explicit Calculation of Roots 03:12 Visualizing the Roots on the Complex Plane Telegram: https://t.me/MathInfinitum TikTok:   / math.infinitum   Instagram: https://www.instagram.com/math_infini...    • Theorem: Every Convergent Sequence is Boun...      • Solving Differential Equation xy\,dx + (x+...      • Does it Converge or Diverge? Integral of 1...      • Integral of 1/x^2: Power Rule with Negativ...      • Complex Analysis: Finding the Laurent Seri...      • Metric Spaces: Definition, Axioms, and Exa...      • Residue Calculation for Higher-Order and S...      • Evaluating Definite Complex Integral from ...      • Linear Differential Equation Solution: (xy...      • Method of Characteristics: Solving PDE (x(...      • Fourier Series Expansion of f(x) = x | Cal...      • Laplace Transform of f(t) = (cos(3t) - 1) ...   #mathematics #complexanalysis #algebra #Manim #ComplexRoots #FundamentalTheoremOfAlgebra #polynomials #education #visualization #mathtutorial #equationsolving