The concept of converting a complex number from cartesian form to polar form and vice-versa.Basic formula and property of complex number is used here.
3. Express each of the following in simplified Cartesian form. a) (v2- V60)0 (V2 + V65)25...
4. Find the complex number, n Cartesian form, such that it satisfies the equation (3- V3)(V3 - 3i)s288V3(Y+i)
4. (15 points) Find all the complex solutions of the equation +(V3-3i)(1+2)40. Express the results in Cartesian form (you may express your answer as a function of k, eg. z = eik cos (kπ/2) + isin(kn/2), k = 0, 1, 2, 3, without explicitly evaluating the expression for each k). 2- 4. (15 points) Find all the complex solutions of the equation +(V3-3i)(1+2)40. Express the results in Cartesian form (you may express your answer as a function of k, eg....
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.
(3) Express in rectangular form all complex solutions to z2+ z +3 = 0.
Question 2 (15 points) (a) Find all the roots of the quadratic equation 2.2 - 2.2 +3, including complex roots. (b) Convert the number u = -27i into polar form, namely in the form u = rei where r = \ul and (c) Find all complex numbers z such that 2+ = -27i, and express all solutions in Cartesian form. argu.
Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for 1 (t) = - 16 - 7 ( g(t) = – 4 – 4t The Cartesian equation is y = Question Help: Message instructor Check Answer a. b. . 1 (t) = t cos(4) 1 vịt) = tsink) 1 (t) = 2 + cos(t) 18(t) = sin(t) = + + cos(t) (t) = + + sin(t) c. 9 d. 2 1...
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...
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
QUESTION 7. [7] Find all solutions to the equation cosh z = i. Express your answer(s) in rectangular (cartesian) form and make a neat sketch showing where the solutions lie in the complex plane. It is acceptable, but not necessary, to consider this exercise as finding and plotting all values of cosh-li.
A space curve is defined by C: T(t)=(5t2+4t)2+4tj+t3k, for t> 0. Find the Cartesian form of the equation for the plane that is perpendicular to the space curve C at the point P: (28, 8, 8). 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 3*x+ 6*z=12-y, or y-x+35*(z-256)=20 Do not use decimal approximations all numbers should be entered as exact expressions,...