ecuacion grado: LAS 4 SOLUCIONES de m⁴ + 4 = 0

In this video, we solve the equation m⁴ + 4 = 0 step by step. Although its expression is extremely simple, it is a fourth-degree equation whose four solutions belong to the set of complex numbers. The real challenge lies not in applying a fourth-degree formula, but in discovering the hidden algebraic structure that allows us to factor it using only two special products. We start with m⁴ + 4 and write the expression in a strategic way. Using the so-called zero trick, we add and subtract the same term to construct a perfect square trinomial. Then we apply a difference of squares and transform the original equation into a product of two second-degree polynomials: (m² + 2m + 2)(m² − 2m + 2) = 0 From here, we use the zero product property and solve the two resulting quadratic equations. During the process, √−4 appears, allowing us to introduce the imaginary unit i and finally obtain the four solutions: m = −1 + i m = −1 − i m = 1 + i m = 1 − i This is a particularly beautiful proof because a seemingly complicated quartic equation ends up being solved using special products, factoring, quadratic equations, and complex numbers. At the end of the video, you'll also find a proposed equation so you can apply a similar strategy yourself. CHAPTERS 00:00 Introduction to the equation m⁴ + 4 = 0 00:53 The two tools we will use 01:24 The algebraic transformation begins 02:15 The zero trick 04:49 Construction of the perfect square trinomial 05:28 Difference of squares 06:28 Factoring the quartic equation 07:28 Applying the zero product property 08:28 Solving the first quadratic equation 10:37 Appearance of the imaginary unit i 11:48 Solving the second quadratic equation 12:39 The four solutions 13:08 Proposed exercise 13:54 Closing music #equations #algebra #complexnumbers #mathwithjuan More equations of degree higher than 3:    • Ecuaciones de Grado Mayor que 3🧮   You'd be helping me a lot if you became a member of MATHEMATICS WITH JUAN    / @matematicaconjuan