Homework Answers
Question 1) Find I = z +2 3z - 2 + 3i 22 + (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
| 1. Let z = 1+ 2i z = -2-2i, z = 3, 24 =i A....
| 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
I. Given Z-2- i and Z2-1 2i. Find the following and express your answer in the...
I. Given Z-2- i and Z2-1 2i. Find the following and express your answer in the form a+ ib (c) Z, Z, (b) 22, +Z, (a).
Exercise 6. (4pts each, 20pts total) Given the complex number zg = -1 + 2i, find...
Exercise 6. (4pts each, 20pts total) Given the complex number zg = -1 + 2i, find m distinct m-th roots (z/m) for the following values of m. You may leave your answer in exponential form. (i) m = 2 (ii) m=4 (iii) m = 10 (iv) m= 45 (v) m = 100
NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the following plan:...
NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the following plan: (i) find the discriminant A of the equation; (ii) write a program for a scientific calculator to obtain the polar form r(cos 0 + i sin 0) of A and the 'first' root + isin COS 2 of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before executing the program, make sure...
③ Let 2,= 2-3 , z = 1+ 2i Find (22) 2 0 ③ compute a...
③ Let 2,= 2-3 , z = 1+ 2i Find (22) 2 0 ③ compute a Ct - ;) e ① & 2 + 1 - ② i + ti
Find the complex numbers w and z which solve the system of equations (-1+i)w + (-2-3i)z...
Find the complex numbers w and z which solve the system of equations (-1+i)w + (-2-3i)z = -12 - 3i (-2+3i)w +(-1+i)z = 0 +10i (Hint: Check your solution by substituting back in)
Consider the vector space P3 (R). Let Z = Span ({1 – x + x2 23,1...
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 )
Let A = [2-3i 3 + 2i [ 5 - 1+i –1 + i 21 1-11...
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
1 Question 3 (4 Marks) show key steps Consider the vector space M2x2(C). i Let Z...
1 Question 3 (4 Marks) show key steps Consider the vector space M2x2(C). i Let Z Span 2 + 3i 2 - 31 2i -2i Is Z? -1+i 10+ 1li s(-
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
| 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
I. Given Z-2- i and Z2-1 2i. Find the following and express your answer in the form a+ ib (c) Z, Z, (b) 22, +Z, (a).
Exercise 6. (4pts each, 20pts total) Given the complex number zg = -1 + 2i, find m distinct m-th roots (z/m) for the following values of m. You may leave your answer in exponential form. (i) m = 2 (ii) m=4 (iii) m = 10 (iv) m= 45 (v) m = 100
NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the following plan: (i) find the discriminant A of the equation; (ii) write a program for a scientific calculator to obtain the polar form r(cos 0 + i sin 0) of A and the 'first' root + isin COS 2 of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before executing the program, make sure...
③ Let 2,= 2-3 , z = 1+ 2i Find (22) 2 0 ③ compute a Ct - ;) e ① & 2 + 1 - ② i + ti
Find the complex numbers w and z which solve the system of equations (-1+i)w + (-2-3i)z = -12 - 3i (-2+3i)w +(-1+i)z = 0 +10i (Hint: Check your solution by substituting back in)
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 )
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
1 Question 3 (4 Marks) show key steps Consider the vector space M2x2(C). i Let Z Span 2 + 3i 2 - 31 2i -2i Is Z? -1+i 10+ 1li s(-
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