Subjects algebra

Satisfy Imaginary

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Satisfy Imaginary


1. First, let's clarify what it means to "satisfy i." Commonly, in mathematics, especially in complex numbers, the imaginary unit $i$ is defined by the property that $$i^2 = -1.$$ 2. To "satisfy i" means to verify or demonstrate that a given expression or solution holds this defining property or is consistent with it. 3. For example, if you have an equation involving $i$, showing that substituting $i$ into the equation yields a true statement demonstrates that the equation "satisfies $i$." 4. Another context is when solving an equation like $$x^2 + 1 = 0,$$ the solutions are $$x = \\pm i$$ because substituting $i$ gives $$i^2 + 1 = -1 + 1 = 0,$$ which satisfies the original equation. 5. In summary, "satisfying $i$" typically means validating the defining properties or verifying solutions that include the imaginary unit $i$ by substitution and simplification.