The imaginary numbers are numbers that result in negative numbers when raised to even powers. An imaginary number is the product of a non-zero real number and iota i where i is square root of -1.
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A number of the form {eq}a+ib {/eq} is known as a complex number, where {eq}i {/eq} is known as iota, which has the value {eq}\sqrt{-1} {/eq}. Iota has some properties such as the square of iota is equal to {eq}-1 {/eq} and the fourth power of iota is 1. ...
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Throughout this work, we use (M, g) to denote a compact connected orientable Riemannian manifold of dimension three with a non-empty smooth boundary. The corresponding volume form and geodesic distance are denoted by d\mu _g(\cdot ) and d_g(\cdot ,\cdot ), respectively. Let \iota _...
Let \iota >0 be arbitrarily small, and fix a compact interval J=[\tau _0,{{\mathcal {T}}}]\subset (s,\infty ). One can take finitely many points \{t_j\}_{j=1}^N\subset J as well as \delta >0 such that \begin{aligned} \sup _{t\in J}\Vert g(t-\varepsilon )-g(...
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