Perform the calculation (8i)3-(8i)2+8i-1. Give your answer in Cartesian form z=x+iy.
Perform the calculation (8i)3-(8i)2+8i-1. Give your answer in Cartesian form z=x+iy.
Question 3 (a) Write the following complex numbers z + iy in polar form z+ iy re giving the angle θ as the sum of its principal argument, (chosen to lie in-r < θ,-r) and an integer multiple of 2π. That is, write θ as θ θp + 2km where k-0, 1, 2, +2Tk +2T k +2T (b) Compute all three values of i1/S and write your answers in the form a + iy.
Use the polar form of the complex number 5 i to find a value in Cartesian form, z = x+iy. Enter the exact answer. Z= 0+iv 5 Edit
transformation. Perform the mappings of lines x- 2 and y 3 under the transformation w = z2 where z = x + iy. Compute the angles between the curves in the u-v plane at the points of intersection. Hence check if the angles between the lines in the z-plane are the same as the angles between the curves in the u-v plane transformation. Perform the mappings of lines x- 2 and y 3 under the transformation w = z2 where...
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. Find in the form x + iy showing details (e) (3 + 4i)^(1/2) (f) ( 1/2 + i√ 3 / 2 )^4 (g) −4+19i / (2+5i)
Resolve the following equation if (have to find z in cartesian form) ZEC (z+3) 2+2 = 3 - 4i
Question 12 (2 marks) Attempt 1 A space curve is defined by C:u)2i+u+3u2k, for u20 Find the Cartesian form of the equation for the plane that is perpendicular to the space curve C at the point where u 1 Your answer should be an equation, expressed in terms of the Cartesian variables x, y and z using the correct syntax. For example: 3*x-2y+5'z-2, or, 2 (x-1)+4 (y-2)+z-1-0, or 3'x+ 6'z-12-y, or y-x+35 (2-256)-20 Do not use decimal approximations all numbers...
A space curve is defined by C:r(u)--2/u!+?+8u2k, for u > 0. Find the Cartesian form of the equation for the plane that is perpendicular to the space curve C at the point where u1 Your answer should be an equation, expressed in terms of the Cartesian variables x, y and z using the correct syntax For example: 3*x-2*y+5*z-2, or, 2*(x-1)+4*(y-2)+z-1-0, or 3x+ 6*z-12-y, or y-x+35*(z-256)-20 Do not use decimal approximations all numbers should be entered as exact expressions, for example...
1. Write f(z) in the form f(x) = u(x, y) +iv(x, y). (a) f(x) = 23+2+1 (b) f(3) = 2,270. Suppose f(z) = x2 - y2 - 2y +i (2x - 2xy), where z = x + iy, and express () in terms of .
Simplify the expression 52 2-1 + zti and give your answer in the form of f(3) 9(2) Your answer for the function f(x) is : 3x + 7 Your answer for the function g(x) is: (x+1)(2-1) Submit Question