Write -V3+ i in polar and exponential forms. Write 2 = 3 COS + e) in...
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,...
help me question 3 stated 1 V3 1, Determine the polar coordinates of the point (z,y) 2, Determine the line tangent to the polar curve T 1+cos θ when θ Be sure to write your line in the form y mx +b 3. Determine the area enclosed by the polar curve cos(28), 0 θ < 2π r Determine the area of the inner loop of the the polar curve stated 1 V3 1, Determine the polar coordinates of the point...
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.
-1-1 arctan n n" n!5* (c) Find the interval of convergence and radius of convergence for )0301 i )e-3r) (d) Use the geometric series to write the power series expansion for i. f(1)- 2-4r, centered at a = 0. i.)4 centered at a-6. (e) Write the first 4 nonzero terms of the Maclaurin expansion for i, f(z) = z2 (e4-1) ii. /(x) = cos(3r)-2 sin(2x). (0) Use the Taylor Series definition to write the expansion for f(a)entered at (8) Use...
Plot the complex number on the complex plane and write it in polar form and in exponential form. 3-41 Plot the complex number on the complex plane. Write the complex number 3 - 4 i in polar form. Select the correct choice below and fill in the answer box(es) within your choice. (Simplify your answer. Type an exact answer for r, using radicals as needed. Type any angle measures in radians, rounding to three decimal places as needed. Use angle...
Convert the polar equation to rectangular form. r = 3 cos e
1)Polar form and 11 Exponential form Hint: Localise the complex vector in the complex plane. Define the modulus r and the argument, then convert to: Polar form: z = r(cose + i sine) = rcise Exponential form z = eie
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
Plot the point given by the polar coordinates. 1 (19) 2. Convert each point from polar to Cartesian coordinates. -Зл 71 7. 5, 9. 6.25, 3,7) Convert each point from Cartesian to polar coordinates. 14. (-6, V3) 13. (-3,0)
Write each of the given numbers in the polar form re^(i(theta)), -pi < theta less than or equal to pi a) (cos(-2pi/9)+isin(-2pi/9))^3 r=? theta=? b) (2-2i)/(-sqrt(3)+i) r=? theta=? c) 2i/(3e^(8+i)) r=? theta=? Sqrt= square root