Complex numbers can represent real world data, in a way that may be more complicated (or near impossible), if trying to represent with just real numbers. I cannot post links in the answer, but recently the Numberphile channel on YouTube posted a video on Quaternions. Also there used to be a really cool article with an interactive animation, showing what imaginary numbers represent on (picomonster dot com) but it no longer works.
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x^7 + 15x^6 + 86x^5 + 240x^4 + 359x^3 + 345x^2 + 274x + 120 = 0
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the maximum number of solutions to an euation is equal to the highest power expressed in the equation. 2x^2=whatever will have 2 answers
You need to be more specific. A quadratic equation will have 2 solutions. The 2 solutions can be equal (such as x² + 2x + 1 = 0, solution is -1 and -1). If one of the solutions is a real number, then the other solution will also be a real number. If one of the solutions is a complex number, then the other solution will also be a complex number. [a complex number has a real component and an imaginary component]In the equation: Ax² + Bx + C = 0. The term [B² - 4AC] will determine if the solution is a double-root, or if the answer is real or complex.if B² = 4AC, then a double-root (real).if B² > 4AC, then 2 real rootsif B² < 4AC, then the quadratic formula will produce a square root of a negative number, and the solution will be 2 complex numbers.If B = 0, then the numbers will be either pure imaginary or real, and negatives of each other [ example 2i and -2i are solutions to x² + 4 = 0]Example of 2 real and opposite sign: x² - 4 = 0; 2 and -2 are solutions.
The complex number of the equation z = x + iy is x.