1. Compute the magnitude of the following complex numbers (a) 1+i (b) 1-i (c) (d) 3+14...

 

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1. Compute the magnitude of the following complex numbers (a) 1+i (b) 1-i (c) (d) 3+14 1+i (e) 3em 2. Evaluate the quantity e for each of the given values of 0. Give your answer in rectangular form and plot the points on the unit circle in the complex plane: (a) 0 = 0 (b) 0= π/6 (c) 0 = π/4 (d) 0 = π/3 (e) 0 = π/2 (f) 0 = 3π/4 (g) 0 = T (h) 0=5/4 (i) 0=3π/2 (j) 0=7π/4 (k) 0 = 2π (1) 0=9π/4 (m) 0 = 5/2 (n) 0 = π/2+6π 3. Given the column vectors [2+31] -D---- 7 -2i (a) |x) + y) (b) (xx) (c) (yly) (d) (2x) (d) |x) (r (e) x)(z 4. Solve the equation |x) = compute the following quantities (a) Show that Z is unitary (b) Given the column vectors: (a) Draw your answer in the complex plane (b) Give your answer in both rectangular and polar form 5. Consider the following matrix: Fjk = 1 r = 1 VN 1 12xjk EN Z= -69 M-HD-H |0) = (1) compute Z10) and Z11). 6. Consider a Nx N matrix F whose elements are defined as follows: j,k= 0, 1,, N-1 = (a) Write out the matrix F when N = 2 and show that F is unitary. (b) Write out the matrix F when N = 4 and show that F is unitary. 1. Compute the magnitude of the following complex numbers (a) 1+i (b) 1-i (c) (d) 3+14 1+i (e) 3em 2. Evaluate the quantity e for each of the given values of 0. Give your answer in rectangular form and plot the points on the unit circle in the complex plane: (a) 0 = 0 (b) 0= π/6 (c) 0 = π/4 (d) 0 = π/3 (e) 0 = π/2 (f) 0 = 3π/4 (g) 0 = T (h) 0=5/4 (i) 0=3π/2 (j) 0=7π/4 (k) 0 = 2π (1) 0=9π/4 (m) 0 = 5/2 (n) 0 = π/2+6π 3. Given the column vectors [2+31] -D---- 7 -2i (a) |x) + y) (b) (xx) (c) (yly) (d) (2x) (d) |x) (r (e) x)(z 4. Solve the equation |x) = compute the following quantities (a) Show that Z is unitary (b) Given the column vectors: (a) Draw your answer in the complex plane (b) Give your answer in both rectangular and polar form 5. Consider the following matrix: Fjk = 1 r = 1 VN 1 12xjk EN Z= -69 M-HD-H |0) = (1) compute Z10) and Z11). 6. Consider a Nx N matrix F whose elements are defined as follows: j,k= 0, 1,, N-1 = (a) Write out the matrix F when N = 2 and show that F is unitary. (b) Write out the matrix F when N = 4 and show that F is unitary.

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1 a Z 1 2 b Z1i C 17Z1 11 e d Z 121 1 1 2 Z ... View the full answer