Question 2. (a) Find all solutions : є C of the equation tan(z) = (1 + iVT)/4. (b) Verify that the solutions you claitm to have discovered do actually satisky the oqatio (c) Evaluate the following contour integral: dz tan(a) - 1-iv7 Question 2. (a) Find all solutions : є C of the equation tan(z) = (1 + iVT)/4. (b) Verify that the solutions you claitm to have discovered do actually satisky the oqatio (c) Evaluate the following contour integral:...
By writing z in the form z = a + bi, find all solutions z of the following equation: z2 - 3z + 1 + i = 0.
2: (a) Find all solutions (x, y) = Z2 to Pell's Equation x2 – 29 y2 = 1. (b) Find all solutions (x, y) € Z to the Pell-like equation x2 - 21 y2 = 4.
Find the exact radian solutions for all which are solutions of the equation. V3+ 2 sin 20 = 0 (4) - Use the quadratic formula to solve for the solutions of the equation in the interval [0°, 360°). Approximate the solutions to the nearest 0.1°. 5sin? x + 2 sin x – 1 = 0
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.
2. Find power series solutions y z" Σ anr" of the following equation centered at 0 where-0 is a regular singular point. (a) Find the indicial equation for r, and solve for the two roots. Note that the indicial equation can be obtained from the coefficients of the term Pick the larger root and find the first seven terms of your power series solutions, i.e., (b)
Find all real solutions of the equation (2 – 6)? = 4. 21 = and 12 with i < 22
Find all solutions of the given equation 2- 6x3 + 3 = 0
Find all solutions of the given equation
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....