Question 9 10 pts Let z = 2/3 - 2i. calculate Hint: First draw a sketch....
Problem 1.4 (a) Let 2 = 3e32"/3. Convert z to Cartesian form. (b) Let z = 6 - 23. Convert z to polar form. (c) Let 2 = 1-. Calculate 25. (d) Let z be a complex number and 23 = V3+j. Find all possible values of 2.
Let Z! = 3H4, Z2-5-2, Z,--3-12, Z4--10-j6, and Z5--6-3. 1. Calculate Z1 + Z2 in rectangular form. 2. Calculate Z1 - Z2 in rectangular form. 3. Calculate Z3 + Z4 in polar form. 4. Calculate Za - Z5 in polar form. 5. Calculate Z1Z2-Z3 in rectangular form. 6. Find ZsZ7 in polar form. 7. Find Z7Zs in rectangular form. 8. Find ZsZs+Z7 in rectangular form Reduce the following to rectangular form. 10. Z1/Z2
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NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the following plan: (i) find the discriminant A of the equation; (ii) write a program for a scientific calculator to obtain the polar form r(cos 0 + i sin 0) of A and the 'first' root + isin COS 2 of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before executing the program,...
10. Stokes Theorem and Surface Integrals of Vector Fields a Stokes Theorem:J F dr- b. Let S be the surface of the paraboloid z 4-x2-y2 and C is the trace of S in the xy-plane. Draw a sketch of curve C in the xy-plane. Let F(x,y,z) = <2z, x, y, Compute the curl (F) c. d. Find a parametrization of the surface S: G(u,v)ーーーーーーーーーーーーー Compute N(u,v) e. Use Stokes' Theorem to compute Jc F dr
10. Stokes Theorem and Surface...
Question 3. (20 pts) Let A= -3 9-27 2 -6 48 3 -9 -2 2 Question 4. (15 pts) Let the matrix A be the same as in Question 3 (1). Find the rank of A (2). Find the dimensions of Nul(A) and (0) (3). How do the dimensions of Nul(A) and Call relate to the mber of columns of A?
Question 3. (20 pts) Let A= -3 9-27 2 -6 4 8 3 -9 -2 2 Find a basis for Col(A) and a basis for Nul(A). Question 4. (15 pts) Let the matrix A be the same as in Question 3. (1). Find the rank of A. (2). Find the dimensions of Nul(A) and Col(A). (3). How do the dimensions of Nul(A) and Col(A) relate to the number of columns of A?
A= 9 2 3 -9 -2 Question 4. (15 pts) Let the matrix A be the same as in Question 3 (1). Find the rank of A. (2). Find the dimensions of Nul(A) and Col(A). (3). How do the dimensions of Nul(A) and Col(A) relate to the number of columns of A?
D | Question 3 4 pts Solve the following system of equations using Gauss-Jordan elimination: 82-5y-5z =-11 The solution of this system of equations has the form z :-az + b, y # cz + d where z can be any real number in the spaces below, put the value of a in the first blank, the value of b in the second blank, the value of c in the third blank, and the value of d in the fourth...
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Question 9 10 pts Let A-(3.1i-2.33+1.9k) cm and B have components B, -2.7 cm, B,-1.5 cm, with no y component. What is A+B? O 1.21 cm (0.4i - 2.33+3.4k) cm CTL O 7.39 cm 3.9 cm o (5.8i -2.33+0.4k) cm Question 10 10 pts What is the magnitude (in crn of the vector (-101 + 2 8 . 2.3 k) cm? (Here k is the unit vector in the z direction .. there does not appear to be...
question #6
1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1 (d) r2+y-22+1 0 (e) -y2+-1 0. 2. Find an equation for the surface consisting of all points that are- point (1,-3, 5) and the plane r = 3. 3. Sketch the curve F(t)<t cos(t), t sin (t), t > 4. Find a vector equation that represents the curve of the intersec r2y =9 and the plane y + z = 2. 5. Find a...