Simplify: 5 + 3i 1 + 2i
Write the expression in standard form. 2i-(-6 +19) 2i-(-6 + 19i) = (Simplify your answer. Type your answer in the form a + bi.)
wnch S puytes to 3 2. Prove by induction on n that Li-1 (2i-1) (2i+1) 1 for n 1,2, 3, .... 2n+1
6 |and 5 2i 1 + has complex eigenvalue, eigenvector pairs (5 + 2i, (j) A 5 - 4 Draw the phase portrait of the linear system X' = AX. Make sure to label relevant features and to include arrows to indicate directions of trajectories. 6 |and 5 2i 1 + has complex eigenvalue, eigenvector pairs (5 + 2i, (j) A 5 - 4 Draw the phase portrait of the linear system X' = AX. Make sure to label relevant...
| 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
4. Working within an eigenbasis for A. 1 2i A = -2i 1 a) Given matrix A, solve for the eigenbasis, {le), le2)} (remember: le;) are column vectors). Note: I expect you to pull out a common factor so that the first entry in the vectors is positive and real. b) Solve for the projection matrices: le) (e;]-. 2 c) Explicitly show the result of the operation:le) (el. i-1 d) Explicitly show the result of the operation: , ; ei)...
4. Working within an eigenbasis for A A-[- 1 2i 2i 1 a) Given matrix A, solve for the eigenbasis, {lei) , le2)} (remember: le) are column vectors) Note: I expect you to pull out a common factor so that the first entry in the vectors is positive and real b) Solve for the projection matrices: le.) (eal 2 e) Explicitly show the result of the operation:le) (el i1 2 e) (el (where A are the eigenvalues of d) Explicitly...
Find all the values of (1 + 2i)}.
6 -1 1 and 5 2i 1 (j) A 5 has complex eigenvalue, eigenvector pairs (5 + 2i 4 - 1 - 2i 1+2i Draw the phase portrait of the linear system X' = AX. Make sure to label relevant features and to include arrows to indicate directions of trajectories 6 -1 1 and 5 2i 1 (j) A 5 has complex eigenvalue, eigenvector pairs (5 + 2i 4 - 1 - 2i 1+2i Draw the phase portrait of the...
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors 2-2i and -2+2i Write the solution to the linear system AF in the following forms A. In eigenvalueleigenvector form r(t) B. In fundamental matrix form z(t) v(t) C. As two equations: (write "c1* and "c2" for ci and C2) a(t)- v(t)- (1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors 2-2i and -2+2i Write the solution to the linear system AF in the...