Use the algebraic identity: {eq}(a+b)^2=a^2+2ab+b^2 {/eq} {eq}(2+3i )^2=2^2+2(2)(3i )+(3i)^2=4+12i+9i^2=4+12i-9 {/eq} where {eq}i^2=-1 {/eq}. {eq... Learn more about this topic: Modulus of a Complex Number | Concept, Formula & Examples ...
The length from the origin and the complex plane, which is denoted by a complex number is known as the magnitude of the complex number. It is the same as finding the absolute value of the complex number. The formula for finding the magnitude of {eq}z=a+bi {/eq} is given by: $$\...
Given a complex number represented as “I + jQ”, the magnitude is: sqrt(I**2 + Q**2). Unfortunately, the square-root operation in this formula is inherently slow and complicated to calculate, either in software or in hardware. For applications which do not require a full-precision magni...
Letz=x+iy, what is the magnitude ofez¯? What is the imaginary component ofez¯? e: Letz=x+iybe the complex number then, x and y are the real and imagenary pary of Z. Hence every real number is a complex number with imagenary part zero. ...
For complex numbers, which have both a real and imaginary component the calculation is more complicated. Generally the magnitude of a complex number is defined by its modulus, the square root of the product of the complex number and its complex conjugate: {eq}|3 + 4i| = \sqrt{(3 \times...
High-speed magnitude approximation algorithms for complex vectors are discussed intensively. The performance and the convergence speed of these approximation algorithms are analyzed. For the polygon fitting algorithms, the approximation formula under the least mean square error criterion is derived. For the...
In order to systematically advance our understanding of the minimum magnitude limit (Mmin) in the probabilistic seismic hazard analysis (PSHA) calculations
The stress disturbances induced by deep tunnel excavation are a key factor leading to the instability and failure of surrounding rock. To investigate the stress evolution in surrounding rock, this study utilizes a physical simulation system for deep cave
Abstract:High—spedmagnitudeapproximationalgorithmsforcomplexvectorsarediscussedintensively.Thep~rfor. manceandtheconvergencespeedoftheseapproximationalgorithmsareanalyzed.Forthepolygonfittingalgorithms,the approximationformulaundertheleastmeansquareerr0rcriterionisderived.Fortheiterativealgorithms.amodified ...
respectively. The list of household numbers from a survey database was used as a sampling frame. Based on the proportionate allocation formula, from Chacha town 126 and Debreberhan 432 participants were recruited by using a simple random sampling technique. The lottery method was used to identify...