Two complex values are z1=8 + 8i, z2=15 + 7 i. z1∗ and z2∗ are the complex conjugate values. Any complex value can be expessed in the form of a+bi=reiθ. Find r and θ for z1z2∗. Find r and θ for z1/z2∗? Find r and θ for (z1−z2)∗/z1+z2∗. Find r and θ for (z1−z2)∗/z1z2∗ Please explain all steps, Thank you

Two complex values are z1=8 + 8i, z2=15 + 7 i. z1∗ and z2∗ are the complex conjugate values. Any complex value can be expessed in the form of a+bi=reiθ. Find r and θ for z1z2∗. Find r and θ for z1/z2∗? Find r and θ for (z1−z2)∗/z1+z2∗. Find r and θ for (z1−z2)∗/z1z2∗ Please explain all steps, Thank you

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section1.10: Cornoonentsofavector

Problem 1.2QQ: Figure 1.19 shows two vectors lying in the xy-plane. Determine the signs of the x- and y-components...

See similar textbooks

Similar questions

What surface is represented by r a = const, that is described if a is a vector of constant magnitude and direction from the origin and r is the position vector to the point P(x1, x2, x3) on the surface?
A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m), (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P1.69. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure 1.69
In Jules Vernes novel, Twenty Thousand Leagues Under the Sea, Captain Nemo and his passengers undergo many adventures as they travel the Earths oceans, a. If 1.00 league equals 3.500 km, find the depth in meters to which the crew traveled if they actually went 2.000 104 leagues below the ocean surface. b. Find the difference between your answer to part (a) and the radius of the Earth, 6.38 106 m. (Incidentally, author Jules Verne meant that the total distance traveled, and not the depth, was 20,000 leagues.)
Math Review Given the equations 507 = 147 Vf cos and 377 = 147 Vf sin , find (a) Vf by using the identity cos2 + sin2 = 1, and (b) by using the inverse tangent function. (Note: Some may consider it easier finding the angle first, and then Vf by back substitution.) (See Section 6.4.)
A unit of distance used in astronomy is the parsec (pc): 1 pc = 3.26 ly. The distance to the Earths next-nearest star, -Centauri, is 1.3 pc. Find the distance d to -Centauri in light-years and in meters.
At one point in space, the direction of the electric field vector Is given In the Cartesian system by the unit vector . If the magnitude of the electric field vector is E=400.0V/m , what are the scalar components , and of the electric field vector at this point? What is the direction angle of the electric field vector at this point?
A marathon runner completes a 42.188-km course in 2 h, 30 min, and 12s. There is an uncertainty of 25 m in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the percent uncertainty in the elapsed time. (C) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?
Two points in the xy plane have Cartesian coordinates (2.00, 4.00) m and (3.00, 3.00) m. Determine (a) the distance between these points and (b) their polar coordinates.
A calculator displays a result as 1.365 218 0 X 107 kg. The estimated uncertainty in the result is 2%. How many digits should be included as significant when the result is written down? (a) zero (b) one (c) two (d) three (e) four
Two aircraft approaching an aircraft carrier are detected by radar. The first aircraft is at a horizontal distance of 34.3 km in the direction 42.0 north of east and has an altitude of 2.40 km. The second aircraft, at half this altitude, is at a horizontal distance of 42.6 km in the direction 37.0 north of east. What is the distance separating the two aircraft? Hint: Use a coordinate system with the x axis pointing east, the y axis pointing north, and the z axis in the vertical direction.
Find (a) the x- and (b) y-components of R = 2A B if A has components Ax = 15.0 m and Ay = 12.0 m whereas B has components Bx = 24.0 m and By = 8.00 m. (See Section 3.2.)
Calculate the result for each of the following cases using the correct number of significant figures. a. 3.07670 10.988 b. 1.0093 105 9.98 104 c. 5.44231064.008103