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8) (20 pts) Express (1 + D) (+) in the form a +jb. Write down the...
IME Express (1+1)(1+) in the form a tib Write down the principal value. Hint z = g'
Problem 4 (20 PTS) For the given function: 2(,y) = re (1) (8 PTS) Determine 2x , zy, Zry, and Zyz. (2) (4 PTS) State whether the conclusion of Clairaut's theorem holds for z(x, y) and explain your answer. (3) (8 PTS) Determine and write down the equation of the tangent plane to the surface : at the point P(1,0,1). Give the equation in standard form, i.e. in the form Ax+By+C2 = D.
1. Find (0.9 + j1.2)^0.3 and express it in the form a +jb. 2. Let x[n] = u[n+5] -u[n-2] and h[n] = u[n+3] - u[n-1]. Over what range of n will the convolution of x and h be non-zero?
3. Complex numbers and math a) Express z=-6 8 in polar form b) Express -1 in polar form c Express z--3e in rectangular form. d) Express z-(2+j) in rectangular form. e) For the two complex numbers z, (6-j4) ad z(-2+j1) determine in polar form. f) lf z=(-84%) determine Teal! (z*)"! in polar form.
1(a) Find the square roots of the complex number z -3 + j4, expressing your answer in the form a + jb. Hence find the roots for the quadratic equation: x2-x(1- 0 giving your answer in the form p+ q where p is a real number and q is a complex number. I7 marks] (b) Express: 3 + in the form ω-reje (r> 0, 0 which o is real and positive. θ < 2π). Hence find the smallest value of...
1. (40 points) Write down the phasor representation for each of the following signals a. (5 pts) x, () 12cos(21) b. pts) x(1)-20cos(3t+45) c. (5 pts)x,(t)-10sin(21 + 300) d. (5 pts) x,(t)-35cos(20+22 sinQ2 +45") e. (10 pts) )- d 135cos(21)+22 sin(2i+4')leas ao express the result in the time domain. f (10 pts) ,)-[B5cos(21)+22sin(2r +45°ydr. Please also express the result in the time domain. Notes: Phasors are ideal for steady-state analysis of sinusoidal signals at a fixed frequency, so we cannot...
By ignoring the electron-electron repulsion write down the approximate form of the first excited state of Helium. What is the probability density? (Hint: It's a function of both electrons coordinates and remember Z!)
By ignoring the electron-electron repulsion write down the approximate form of the first excited state of Helium. What is the probability density? (Hint: It's a function of both electrons coordinates and remember Z!)
QUESTION 4. (25 pts) Write down the Normal form of the following game. 2 Х + (11,9) 1 Y (100, 17) V E 2 (0,0) A W (0,3) 1 (6,-8) V B C 2 W (4, 12) (11, 14)
Please do 2,4, and 10
d s and y when n the Argand dilagram, the origin is the numbers representing the other vertices Spress 2 + /S and 1 -12 in potar torm and a 60 tex of the triangle is the point 3 -NS. Find the comps centre ot an epuailateral trang 2 Express the result in th e form a jo and in espoment form. nd the fnith roots of -3+3 in polar form and in esponential torm...
By ignoring the electron-electron repulsion write down the approximate form of the first excited state of Helium. What is the probability density? (Hint: It’s a function of both electrons coordinates and remember Z!).