Complex number review Determine the magnitude and phase in degrees (with sign) o

Question

Complex number review Determine the magnitude and phase in degrees (with sign) of the following complex numbers. (a, b, c, d, e, f are positive real numbers a = 0.35, b = 3.7, c = 2.9, d = 4.6, e = 1.3, f = 3.1). I strongly advise you to go further than just relying on software. For example some calculator programs require you to just put MAG or something similar in front of a complex number to get the magnitude. This may get you the answers to the first part of this homework but you will learn very little and be disadvantaged later in the course. Try to figure out the symbolic forms of the magnitude and phase for each of the complex numbers given before you obtain a numeric value. Magnitude z = a + jb Phase z = a + jb Magnitude z = a - jb Phase z = a- jb Magnitude z = (a + jb)(c + jd) Phase z = (a + jb)(c + jd) Magnitude z = 1/(a + jb)(c + jd) Phase z = 1/(a + jb)(c + jd) Magnitude z = (a + jb)(a - jb)/(c + jb)(e + jf) Phase z = (a + jb)(a - jb)/(c + jb)(e + jf) Magnitude z = a + jb/(c + jd)(e - jf) Phase z = (a + Jb)/ (c + Jd){e - jf ) Magnitude z =(a + jb)/c(d + je) Phase z = (a + jb)/c(d +je) Magnitude z = -jf Phase z = -jf Magnitude z = -1/ (ja) Phase Z = -1/(ja) Magnitude z = (- ja)(jb)(jc)(jd) Phase z = (-ja)(jb)(jc)(jd)

Explanation / Answer

Please , rate five star. The answer can be calculated with above provided info. The answers are. a = 0.35,b = 3.7 , c = 2.9, d = 4.6, e = 1.3, f = 3.1 1) |Z| = sqrt (a^2 + b^2) = 3.718 2) phase z = tan-1(b/a) = 84.59 deg 3) |z| = sqrt (a^2 + b^2) = 3.718 4) phase z = tan-1(-b/a) = -84.59 deg 5) |z| = 3.718* sqrt (c^2 + d^2) = 20.217 6) z = (ac-bd) + j(ad+bc) phace z = tan-1(-0.771) = -37.63 deg 7) |z| = 1/20.217 = 0.049 8) phase z = 37.63 deg 9)z= -0.426 - .0763j |z| = 0.873 10) phase z = 49.93 deg

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