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4. (15 points) Find all the complex solutions of the equation +(V3-3i)(1+2)40. Express the result...
Question 2 (15 points) (a) Find all the roots of the quadratic equation 2.2 - 2.2...
Question 2 (15 points) (a) Find all the roots of the quadratic equation 2.2 - 2.2 +3, including complex roots. (b) Convert the number u = -27i into polar form, namely in the form u = rei where r = \ul and (c) Find all complex numbers z such that 2+ = -27i, and express all solutions in Cartesian form. argu.
NAME: Q1. (30pts) Solve the quadratic equation 22-(1-4i)2-9+3i 0 by realizing the following plan: (i) find...
NAME: Q1. (30pts) Solve the quadratic equation 22-(1-4i)2-9+3i 0 by realizing the following plan: (i) find the discriminant A of the equation: (i) write a program for a scientific calculator to obtain the polar form r(cos 0 + isin @i of A and the 'first root + isin- cos 2 of degree two of A; (ii) execute the program, fix the results, find another root A of A of degree two (before executing the program, make sure that your caleulator...
QUESTION 7. [7] Find all solutions to the equation cosh z = i. Express your answer(s)...
QUESTION 7. [7] Find all solutions to the equation cosh z = i. Express your answer(s) in rectangular (cartesian) form and make a neat sketch showing where the solutions lie in the complex plane. It is acceptable, but not necessary, to consider this exercise as finding and plotting all values of cosh-li.
Solve, finding all solutions. Express the solutions in both radians and degrees. cos x= - Express...
Solve, finding all solutions. Express the solutions in both radians and degrees. cos x= - Express the solutions in radians. Select the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. There is one solution on [0,21) at x = . Solutions are of the form x + 2km, where k is an integer. (Simplify your answer. Type an exact answer, using a as needed. Use integers or fractions for any numbers...
Solve, finding all solutions. Express the solutions in both radians and degrees. 1 sin x= 2....
Solve, finding all solutions. Express the solutions in both radians and degrees. 1 sin x= 2. Express the solutions in radians. Select the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. There is one solution on (0.28) at x = Solutions are of the form x + 2kt, where k is an integer. (Simplify your answer. Type an exact answer, using r as needed. Use integers or fractions for any numbers...
4. simplify the complex-valued expression: V3-j6 4-1) [0.1 points] give the answer in rectangular form 4-2)...
4. simplify the complex-valued expression: V3-j6 4-1) [0.1 points] give the answer in rectangular form 4-2) [0.1 points] give the answer in polar form. The angle should be between 0 and 2n.
1 2 NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the...
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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,...
4. (15 marks) Consider the following equation: where i denotes the complex number satisfying i2--1 (a)...
4. (15 marks) Consider the following equation: where i denotes the complex number satisfying i2--1 (a) Rewrite the number -i in the exponential form and transform equation (5) into (b) Solve (6) to get the five solutions wo, ..., wa and draw them on the Argand diagramme (c) Show that wo··· , ua are the eigenvalues of the following real-valued matrix 0 0 0 0 0 cos(2m/5) A-10 -sin2(2π/5) 0 0 cos(2π/5) 0 0 0 2cos(4π/5) 2 Hint: compute the...
02. (2). If |2-3|=|z+il. (1). Use an algebraic method to find a Cartesian equation of the...
02. (2). If |2-3|=|z+il. (1). Use an algebraic method to find a Cartesian equation of the locus of 2 (11) Sketch the locus of zon an Argand diagram. (6). If are 9- (1). Sketch the locus of P(x,y) which is represented by z on an Argand diagram (i). Find the Cartesian equation of this locus. (c). Given that the complex number z=x+iy where x,y e Rssatisfies the equation 12-12-51 = 3, find the minimum value and the maximum value of...
(1/2 Points] DETAILS PREVIOUS ANSWERS MCKTRIG8 6.1. Solve the following equation for all radian solutions and...
(1/2 Points] DETAILS PREVIOUS ANSWERS MCKTRIG8 6.1. Solve the following equation for all radian solutions and if ost< 2. Give there is no solution, enter NO SOLUTION.) 8 sint - V3 = 6 sint (a) all radian solutions (Let k be any integer.) t = TT 3 + 2tik, 211 3 + 2nkrad (b) Ost< 22 rad Need Help? Read It Watch It Talk to a Tutor Talk to a Tutor
Question 2 (15 points) (a) Find all the roots of the quadratic equation 2.2 - 2.2 +3, including complex roots. (b) Convert the number u = -27i into polar form, namely in the form u = rei where r = \ul and (c) Find all complex numbers z such that 2+ = -27i, and express all solutions in Cartesian form. argu.
NAME: Q1. (30pts) Solve the quadratic equation 22-(1-4i)2-9+3i 0 by realizing the following plan: (i) find the discriminant A of the equation: (i) write a program for a scientific calculator to obtain the polar form r(cos 0 + isin @i of A and the 'first root + isin- cos 2 of degree two of A; (ii) execute the program, fix the results, find another root A of A of degree two (before executing the program, make sure that your caleulator...
QUESTION 7. [7] Find all solutions to the equation cosh z = i. Express your answer(s) in rectangular (cartesian) form and make a neat sketch showing where the solutions lie in the complex plane. It is acceptable, but not necessary, to consider this exercise as finding and plotting all values of cosh-li.
Solve, finding all solutions. Express the solutions in both radians and degrees. cos x= - Express the solutions in radians. Select the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. There is one solution on [0,21) at x = . Solutions are of the form x + 2km, where k is an integer. (Simplify your answer. Type an exact answer, using a as needed. Use integers or fractions for any numbers...
Solve, finding all solutions. Express the solutions in both radians and degrees. 1 sin x= 2. Express the solutions in radians. Select the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. There is one solution on (0.28) at x = Solutions are of the form x + 2kt, where k is an integer. (Simplify your answer. Type an exact answer, using r as needed. Use integers or fractions for any numbers...
4. simplify the complex-valued expression: V3-j6 4-1) [0.1 points] give the answer in rectangular form 4-2) [0.1 points] give the answer in polar form. The angle should be between 0 and 2n.
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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,...
4. (15 marks) Consider the following equation: where i denotes the complex number satisfying i2--1 (a) Rewrite the number -i in the exponential form and transform equation (5) into (b) Solve (6) to get the five solutions wo, ..., wa and draw them on the Argand diagramme (c) Show that wo··· , ua are the eigenvalues of the following real-valued matrix 0 0 0 0 0 cos(2m/5) A-10 -sin2(2π/5) 0 0 cos(2π/5) 0 0 0 2cos(4π/5) 2 Hint: compute the...
02. (2). If |2-3|=|z+il. (1). Use an algebraic method to find a Cartesian equation of the locus of 2 (11) Sketch the locus of zon an Argand diagram. (6). If are 9- (1). Sketch the locus of P(x,y) which is represented by z on an Argand diagram (i). Find the Cartesian equation of this locus. (c). Given that the complex number z=x+iy where x,y e Rssatisfies the equation 12-12-51 = 3, find the minimum value and the maximum value of...
(1/2 Points] DETAILS PREVIOUS ANSWERS MCKTRIG8 6.1. Solve the following equation for all radian solutions and if ost< 2. Give there is no solution, enter NO SOLUTION.) 8 sint - V3 = 6 sint (a) all radian solutions (Let k be any integer.) t = TT 3 + 2tik, 211 3 + 2nkrad (b) Ost< 22 rad Need Help? Read It Watch It Talk to a Tutor Talk to a Tutor
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