5. Compute 8 (a) (1+ v3i) using DeMoivre's formula. (b) The five fifth roots of 1 + V3i
5. Compute 8 (a) (1+ v3i) using DeMoivre's formula. (b) The five fifth roots of 1 + V3i
3. Compute all possible values of i', log (-1 + V3i), sin(+ 2i). (Write your answers in the usual a + bi form.)
1. 2. Find u v and the angle between vector u and v for a) u = 2i – 2j + k, v = 3i + 4k b) u = v3i – 7j, v = v3i+j – 2k c) u = 2i +j, v= i + 2j – k
Write and 22 in polar form. (Express) in radians. Letos B<2) 23-13 +1, 22-1+ v3i 22= Find the product 2122 and the quotients and Express your answers in polar form with expressed in radians.) 2322
#1,5,9 and #13,17,21,25 please.
In Exercises 1-12, graph each complex number in the complex plane 3. -2 4i 2 2. 3 5i 7.-3i 8.-5i 6. 7 47 19 7 15 2 11 2 12. 10 10 each complex number in polar form 15. 1 V3i 14. 2 + 2i 16. -3- V3i 3. 1-i 20. -V3+i 18. V5_V5İ 19. V3-3i 17-44i 24. -8-8V3i 22. 2 + Oi 2 23, 2v3-2i 21. 3 +0i V3 1 1 V3 28·16+161 26, 1...
(2) Determine the RADIUS and ANNULUS OF CONVERGENCE of exactly one of the following POWER SERIES: (2.1) (z – 4i)" n2 · [1 + V3i]2n n=1
(2+1) 2 Compute lim
(2+1) 2 Compute lim
all of q1 please, a complex analysis question for complex
numbers etc.
1. (a) Define the principal branch of Log(2). Find Log(1 + V3i). [6 marks] (b) Find all solutions to ex-1 = -ie3. (6 marks) (c) Find all solutions to 25 = 1+i. (8 marks) (d) Describe the image of the circle |z| = 5 under the mapping f(x) = Log(2). [6 marks]
1. Compute Σ2Σ(i + 2j) 2. Compute Σ2 Σ3-2 ()
1 1 a) Compute the length of the curve y = Inx, for 1 < x < 2. b) Compute the area of the surface obtained when rotating the curve in question a) about the y-axis, for 1 < x < 2.