2. Let w = –2V3 – 2i. Evaluate the following: a. [w] b. arg (w) c....
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.
Write -V3+ i in polar and exponential forms. Write 2 = 3 COS + e) in Cartesian form. 6 6 3) Write z = -2+2i in polar and exponential forms. Calculate zll using the exponential form. convert z11 to Cartesian form.
(a) Find Cartesian coordinates for the polar point (-1, -1) and plot the point. (b) Find Polar coordinates with r > 0 and -1 < <a for the Cartesian point (-1, V3) and plot the point. (c) Convert the equation x2 + y2 = x to polar form and sketch the curve. (d) Convert the equation r = 5 csc @ to Cartesian form and sketch the curve.
Question 9 10 pts Let z = 2/3 - 2i. calculate Hint: First draw a sketch. Second, find the modulus and argument of z. Third convert z into polar form and then exponential form. Fourth, use Moivre's theorem to find Moivre's theorem: z" = goh eine
(1 point) The region W is the cone shown below. C The angle at the vertex is /2, and the top is flat and at a height of 5 Write the limits of integration for f dV in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry) (a) Cartesian: With a b d and f eb d Volume (b) Cylindrical: With a= b d and f eb ed f d Volume = (c) Spherical:...
6. Given u= 2 + 31, p= 1 - 2i and w= -3 – 6i where i = V-1 is the imaginary unit. Evaluate the following: A) (u + v B) u + 20 C) 4–3v + 2w D) U E ) uv F) (ulvt G) v/w
Question 3.1 (10 marks) Consider the two complex numbers-V3+i and 2 3 cis(-/3) a) Write 1V3+i in polar form, in terms of its principal argument. b) Use your answer in a) to evaluate z1/21 in polar form, and then convert that into cartesian form. c) Using their polar forms, determine z122 and z2/句in terms of their principal argument. d) Determine (22)2 in polar form, in terms of its principal argument. e) Determine all distinct values of (22)1/3 in polar form,...
please answer all of them thanks!
Exercise 8.4 Let R be the region bounded by y = x, y = 0 and = 1 (a) Write down the double integral for the area of R. (b) Convert your double integral into iterated integral in Cartesian form (Don't evaluate it. It does not matter which order you take. You can integrate x firstly if you prefer to. ) (c) Convert your double integral into iterated integral in Polar form (Don't evaluate...
for r = 5 + 5cosθ A. Graph the polar function. B. Find two polar points that fit your function. (Pick an angle for θ, plug it into your function, and calculate the value of r. Write your answer in the polar coordinates form (r, θ). Repeat for a second point.) C. Find the Cartesian equivalents (x,y) for the two polar points you found in part B. (Use the conversion formulas x = rcosθ and y = rsinθ for converting...
Q3(a) Let W be the region above the sphere x2 + y2 + z2 = 6 and below the paraboloid z = 4 - x2 - y2 as shown in Figure Q5(a) below: Z=4-x-y? x2 + y + z = 6 Figure Q3(a) (i) Find the equation of the projection of Won the xy-plane. (ii) Compute the volume of W using polar coordinates. [16 marks] (b) Using double integral in polar coordinates, compute the following: $$*** (2x+3y) dedy [7 marks]...