Does this equal 2 or 2i?
Do I look at it as 2(-1)^1/6
1. Find the magnitude and phase of the following complex numbers: (a) 5+8i 2+31 (b)-5-8i (c) 3+37 (d) 4+2i 4-2i
Solve by Gaussian elimination with back substitution. (1 - i)X1 + X2X3 - 3= 1-2i (53 +21i) (2 -11i) (-2 + 6i) (35-51) 5+101) +5) (X1, X2, X3) 35 - 5i (b) 3x1+ 1X2+ (1-i)X3= 2+i IX1 4iX2 (-12 +53i) 57 + 8i (24 - 16i) (56 +7i) (x1, X2, X3) - 57+Si (57i) (57+Si) 57 + 8i
Perform the calculation (8i)3-(8i)2+8i-1. Give your answer in Cartesian form z=x+iy.
6. Consider a triangle with vertices at 1, 2 + 2i, 3-i oriented clockwise. (a) Draw the triangle and mark the orientation on its edges. (b) Find a parametrization for each of its edges 6. Note that parametrization of a straight path from ะเ to 22 is:(t)- + t(22-a), 0 1. t
| 1. Let z = 1+ 2i z = -2-2i, z = 3, 24 =i A. Complex arithmetic (20%) | a. Zi + Z2 b. Z1Zz sle Isles B. Determine the principle value of the argument and graph it (20%) a. 21 b. Z2 c. 23 d. 24
Let A = [2-3i 3 + 2i [ 5 - 1+i –1 + i 21 1-11 -1-il -2 ] The set of solutions to the equation Ax = 0 is 22 = [Select] 23+ [Select] 21
If u =<5-i, -3i, 6+2i > and v=< 3, 21, -1-4i >, use the standard inner produc in Cº to determine, <u,v>, ||-||, and || |
1 5. Let A = dz, (2 – 1)2(2 + 2i)3 where I is the circle [2] = 3 traversed once counterclockwise. The following is an outline of the proof that A = 0, justify each statement. Jo Tz – 1)*(x + 2133 (a) For R > 3 show that A = A(R) where A(R) Som 1 (z – 1)2(x + 2i)3 dz, and I'R is the circle (2|| = R traversed once counterclockwise. 21R (b) For R > 3...
6. Given u= 2 + 31, p= 1 - 2i and w= -3 – 6i where i = V-1 is the imaginary unit. Evaluate the following: A) (u + v B) u + 20 C) 4–3v + 2w D) U E ) uv F) (ulvt G) v/w
Exercise 2 Find logz, Logz and z for (i) -2i; i) z = -1+ i; (i Z (iii z 2/(1 3i)
Exercise 2 Find logz, Logz and z for (i) -2i; i) z = -1+ i; (i Z (iii z 2/(1 3i)