Mathematics
Mathematics, 14.07.2019 20:30, lala1196

Write all of the complex numbers that are graphed in the complex plane shown. a: _ + _i b: _ + _i c: _ + _i d: _ + _i

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Предмет
Mathematics, 22.06.2019 07:30, Fvmousdj5
Ece 202: problem set 1 due: june 14, 2019 (friday) the first 3 questions of this homework assignment covers some fundamental mathematical concepts that will play a role in this course. the remaining questions are on basic signals and laplace transforms. 1. a review of complex numbers. (a) compute the magnitude and the phase of the complex numbers −4 +j, and write them in polar form (i.e., of the form rejθ). also, plot the complex number in the complex plane. (b) simplify the complex number 1 4 − √ 1 2 − j √ 2 22 and write them in cartesian form. (c) consider the complex number s = z1z2 · · ·zm p1p2 · · · pn , where each zi is a complex number with magnitude |zi | and phase ∠zi , and each pi is a complex number with magnitude |pi | and phase ∠pi . write the magnitude and phase of s in terms of the magnitudes and phases of z1, z2, . . , zm, p1, p2, . . , pn. 2. a review of differentiation. (a) find df dx for the following functions. i. f(x) = (1−4x) 2 √ x . ii. f(x) = √ 1 + tan x. (b) find dy dx for the equation e x sin y + cos2 x cos y − x 3 = 0.
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Предмет
Mathematics, 27.06.2019 01:30, aide1234564
Which complex number is represented by the point graphed on the complex plane below? –4 + 3i 3 + 4i 3 – 4i 4 + 3i
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Предмет
Mathematics, 30.07.2019 17:20, anna8352
In the following questions, do not evaluate surds (e.g. ? 2). leave them in your answer in that form (e.g. ? ? = 1 ± ? 2). 1. (a) find the vector and cartesian equations of the plane which contains the point a=(2,3,-1) and is perpendicular to the vector n =(1,2,2). what is the perpendicular distance of the plane from the origin? ? (b) a plane has a normal = ? + 2? ? and is a perpendicular distance of 2 from the origin. what are the vector and cartesian equations of the plane? what is the perpendicular distance of the plane from the point b = (3,1,-1)? 2. if ? ? 1 = 1 + 3? ? and ? ? 2 = 1 ? 2? ? express each of the following complex numbers in the form ? ? + where a and b are real numbers (standard form / cartesian form) (a) (2? ? 1 + 1) (b) (3? ? 2 ? 2) (c) ? ? 1? ? 2 (d) , (complex conjugates of ? ? and ? ? )1212 (e) |? ? 1| , |? ? 2| (magnitudes of ? ? 1 and ? ? 2) (f) 1z1 (g) ? ? 1? ? 2 3. if ? ? 1 =2+4? ? and ? ? 2 =4+? ? determine the complex number ? ? 3 =? ? 1? ? 2 . sketch the complex plane to show the positions of all three of these complex numbers. determine the modulus ? ? and (principal value) of the argument ? ? of each of these three complex). 4. solve ? ? 4 = ? 1?
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