. Show that the image of D1(−1 − i) = {z : |z + 1 + i| < 1} under the transformation
w = (3 − 4i)z + 6 + 2i is the open disc D5(−1 + 3i) = {w : |w + 1 − 3i| < 5}.
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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) write the following complex number in polar form : Z=(2√3 + 2i)10 / 1-√3i2) determine when f(z) = Z+2i / z2-9 is analytic3) let u(x,y) coshx costy . find an analytic function f(z), such that u = Re(f(z))4) Solve the equation sinh(2z) = -1.5) evaluate ln ( 2√3 + 2i ) .
Question 1) Find I = z +2 3z - 2 + 3i 22 + (2i - 2)2 - 4i ] dz, C:\z| = 3, CW a. 4πί b. 8πί C. 2πί d. -2π(3 +i) e. 0.0 f. ο g. -4πί h. 6π
10 Find the image of the rectangular region in the 2 – plane formed by joining the points (0,0),(2,0), (2,1),(0,1) in the w – plane under the transformation, = (1 + i)z – 2i Interpret both the regions graphically. =
#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...
Consider the vector space P3 (R). Let Z = Span ({1 – x + x2 23,1 + 2x + 3x2 + 4x3, x + x3}). Is 6+ 7x + 8x2 + 9x3 E Z? . Consider the vector space M2x2(C). 1 1 i ({( 2+3 );( 1+i 2 );( )}) 3i 2 + 2i 3 + 3i Let Z Span 2 + 3i 2 – 31 2i -2i Is -1+i EZ? 10 + 112 )
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16) On a man the town of Morgan Run is due south of Davidson and is south east of Vicksburg. The distance from Morgan Run to Davidson and Vicksburg are 32 and 52 miles respectively. The distance between Davidson and Vicksburg is 42 miles. If a plane leaves Morgan Run to fly to Vicksburg, on what bearing should it travel? 17) A vector v has initial point (3,-6) and terminal point (2, -3). a. Find the component...
two seperate questions multiple choice
Calculate the following: [3+i 2-i [ [ 3 2 2-i| 2 ས 3 2- 2i - 3 2- 2i 2 - 1 Determine the real and imaginary parts of the complex number by first writing the number in standard form. z=(5-3i)(5 + 3i) Re(z) = 30 and Im(z) = 4 Re(z) = 32 and Im(z) = 2 Re(z) = 34 and Im(z) = 6 Re(z) = 34 and Im(z) = 0
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5. Let t be the inversive transformation defined by Determine the image of each of the following generalized circles under : (a) the extended line E U foo], where E is the line with equation y-x (b) the unit circle . 310 5: Inversive Geometry Problem 7 Let be the inversive transformation defined by 2-2i r(z) = 2. 2+2 Use the strategy to determine the image of each of the following...
7. Consider the fractional linear transformation that maps -1 to -2i, 1 to i and i to 0. Determine the image of the unit circle EC 1 the image of the open unit disk (z EC<1), and the image of the interval [-1,1 on the real axis Illustrate with a sketch