Abstract
This chapter presents algebraic inequalities. The algebraic inequalities involve complex numbers, real numbers, and inequalities for sets of complex numbers. The inequalities in real numbers involve different identities such as Lagrange's identity, Cauchy–Schwarz–Buniakowsky inequalities, Minkowski's inequality, and Hölder's inequality. The inequalities in complex numbers pronounce different inequalities, namely, complex Cauchy–Schwarz–Buniakowsky inequality, complex Minkowski inequality, and complex Hölder inequality. If α, 0 are any two real numbers, the complex number z = a + iβ with real part α and imaginary part β has for its modulus |z| a nonnegative number |z| = α2 + β.
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