1) find all value of i^i, and show that they are all real 2) Find all values of log(-1-i) 3) find a) the cube roots of -1 b) the sixth root of i c) the cube roots of 1-i 4) Find (d/dz) i^z
1) find all value of i^i, and show that they are all real
2) Find all values of log(-1-i)
3) find a) the cube roots of -1
b) the sixth root of i
c) the cube roots of 1-i
4) Find (d/dz) i^z
Homework Answers
1.
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1) find all value of i^i, and show that they are all real 2) Find all values of log(-1-i) 3) find a) the cube roots of -1 b) the sixth root of i c) the cube roots of 1-i 4) Find (d/dz) i^z
5. Let V2 be the real cube root of two. Set e: -1+Bi (i) Show that 2, V2e, and 2e2 are the distin...
all of (i) (ii) (iii)
5. Let V2 be the real cube root of two. Set e: -1+Bi (i) Show that 2, V2e, and 2e2 are the distinct roots of 32 (ii) Conclude that the field Q(2,) contains all of the roots of 3 -2. (ii) Find (Q(V2,e):Q]
5. Let V2 be the real cube root of two. Set e: -1+Bi (i) Show that 2, V2e, and 2e2 are the distinct roots of 32 (ii) Conclude that the field Q(2,)...
Show all work for credit General Solution Roots | y(z) = Genz + Cenz Two real roots r T2 One real root r Bi | y(z)-...
Show all work for credit General Solution Roots | y(z) = Genz + Cenz Two real roots r T2 One real root r Bi | y(z)-Geaz cos(ßz) + Ceaz sin(8z) Two complex roots a Form of p | Example f(t) | Example2 Form of f(t) A cos(t)+Bsin(at) 1. Find the general solution to the DE: y" +4y +4y
Show all work for credit General Solution Roots | y(z) = Genz + Cenz Two real roots r T2 One real root...
Find the cube roots of 125 i. Graph each cube root as a vector in the...
Find the cube roots of 125 i. Graph each cube root as a vector in the complex plane. Choose the correct cube roots below. O A. 5(cos 90° + i sin 90), 5(cos 210° + i sin 210°), 5(cos 330° + i sin 330) B. 5(cos 30° + i sin 30%), 5(cos 150° + i sin 150°), 5(cos 270° + i sin 270º) O C. 125(cos 0° + i sin 0%), 125(cos 120° + i sin 120°), 125(cos 240° +...
Show that the equation z 1 has one real root and two other roots which are...
Show that the equation z 1 has one real root and two other roots which are not real, and that, if one of the non-real roots is denoted by w, the other s then . Mark on the Argand diagram the points which represent the three roots and show that they are the vertices of an equilateral triangle.
show all working please 10 Given z = 2 – j2 is a root of 2z'...
show all working please
10 Given z = 2 – j2 is a root of 2z' - 9z2 + 202 - 8 = 0 find the remaining roots of the equation. Find the real and imaginary parts of z when 1 2 1 2 2 + j3 3 - 2 .. Find z = Z4 + z2z3/(z2+z3) when 2, = 2 +j3, z2 = 3 + j4 and 23 = -5+j12. Find the values of the real numbers x and...
6. Let B(2) i + 22 4- 2iz (a) Find the smallest positive real value M...
6. Let B(2) i + 22 4- 2iz (a) Find the smallest positive real value M such that for every z on the closed unit disk D, B(2) <M. [6] (b) A particle on the complex plane is trapped within a wall built along the unit circle. It travels from -i to e3ri/4 and then bouncing from e3mi/4 to 1. Denote by y the curve representing the trajectory of the particle. Without evaluating the integral, show how we can obtain...
6. Sketch the roots. (Approximate) yi To find the nth roots of z rcise: 1. We will getroots 2. The magnitude of the roots is 3. The angle between the roots on the complex plane is 4. The angle of the...
6. Sketch the roots. (Approximate) yi To find the nth roots of z rcise: 1. We will getroots 2. The magnitude of the roots is 3. The angle between the roots on the complex plane is 4. The angle of the first root is
6. Sketch the roots. (Approximate) yi To find the nth roots of z rcise: 1. We will getroots 2. The magnitude of the roots is 3. The angle between the roots on the complex plane is...
Let B(2) = i + 22 4 – 2iz. (a) Find the smallest positive real value...
Let B(2) = i + 22 4 – 2iz. (a) Find the smallest positive real value M such that for every z on the closed unit disk D, 5B() < M. [6] (b) A particle on the complex plane is trapped within a wall built along the unit circle. It travels from –i to e3ti/4 and then bouncing from e3ti/4 to 1. Denote by y the curve representing the trajectory of the particle. Without evaluating the integral, show how we...
Let B(2) = i + 22 4 – 2iz. (a) Find the smallest positive real value...
Let B(2) = i + 22 4 – 2iz. (a) Find the smallest positive real value M such that for every z on the closed unit disk D, 5B() < M. [6] (b) A particle on the complex plane is trapped within a wall built along the unit circle. It travels from –i to e3ti/4 and then bouncing from e3ti/4 to 1. Denote by y the curve representing the trajectory of the particle. Without evaluating the integral, show how we...
6. Let B(2) = i + 2z 4 - 2iz (a) Find the smallest positive real...
6. Let B(2) = i + 2z 4 - 2iz (a) Find the smallest positive real value M such that for every z on the closed unit disk D, |B() < M. [6] (b) A particle on the complex plane is trapped within a wall built along the unit circle. It travels from –i to e3ri/4 and then bouncing from e3vi/4 to 1. Denote by y the curve representing the trajectory of the particle. Without evaluating the integral, show how...
all of (i) (ii) (iii)
5. Let V2 be the real cube root of two. Set e: -1+Bi (i) Show that 2, V2e, and 2e2 are the distinct roots of 32 (ii) Conclude that the field Q(2,) contains all of the roots of 3 -2. (ii) Find (Q(V2,e):Q]
5. Let V2 be the real cube root of two. Set e: -1+Bi (i) Show that 2, V2e, and 2e2 are the distinct roots of 32 (ii) Conclude that the field Q(2,)...
Show all work for credit General Solution Roots | y(z) = Genz + Cenz Two real roots r T2 One real root r Bi | y(z)-Geaz cos(ßz) + Ceaz sin(8z) Two complex roots a Form of p | Example f(t) | Example2 Form of f(t) A cos(t)+Bsin(at) 1. Find the general solution to the DE: y" +4y +4y
Show all work for credit General Solution Roots | y(z) = Genz + Cenz Two real roots r T2 One real root...
Find the cube roots of 125 i. Graph each cube root as a vector in the complex plane. Choose the correct cube roots below. O A. 5(cos 90° + i sin 90), 5(cos 210° + i sin 210°), 5(cos 330° + i sin 330) B. 5(cos 30° + i sin 30%), 5(cos 150° + i sin 150°), 5(cos 270° + i sin 270º) O C. 125(cos 0° + i sin 0%), 125(cos 120° + i sin 120°), 125(cos 240° +...
Show that the equation z 1 has one real root and two other roots which are not real, and that, if one of the non-real roots is denoted by w, the other s then . Mark on the Argand diagram the points which represent the three roots and show that they are the vertices of an equilateral triangle.
show all working please
10 Given z = 2 – j2 is a root of 2z' - 9z2 + 202 - 8 = 0 find the remaining roots of the equation. Find the real and imaginary parts of z when 1 2 1 2 2 + j3 3 - 2 .. Find z = Z4 + z2z3/(z2+z3) when 2, = 2 +j3, z2 = 3 + j4 and 23 = -5+j12. Find the values of the real numbers x and...
6. Let B(2) i + 22 4- 2iz (a) Find the smallest positive real value M such that for every z on the closed unit disk D, B(2) <M. [6] (b) A particle on the complex plane is trapped within a wall built along the unit circle. It travels from -i to e3ri/4 and then bouncing from e3mi/4 to 1. Denote by y the curve representing the trajectory of the particle. Without evaluating the integral, show how we can obtain...
6. Sketch the roots. (Approximate) yi To find the nth roots of z rcise: 1. We will getroots 2. The magnitude of the roots is 3. The angle between the roots on the complex plane is 4. The angle of the first root is
6. Sketch the roots. (Approximate) yi To find the nth roots of z rcise: 1. We will getroots 2. The magnitude of the roots is 3. The angle between the roots on the complex plane is...
Let B(2) = i + 22 4 – 2iz. (a) Find the smallest positive real value M such that for every z on the closed unit disk D, 5B() < M. [6] (b) A particle on the complex plane is trapped within a wall built along the unit circle. It travels from –i to e3ti/4 and then bouncing from e3ti/4 to 1. Denote by y the curve representing the trajectory of the particle. Without evaluating the integral, show how we...
Let B(2) = i + 22 4 – 2iz. (a) Find the smallest positive real value M such that for every z on the closed unit disk D, 5B() < M. [6] (b) A particle on the complex plane is trapped within a wall built along the unit circle. It travels from –i to e3ti/4 and then bouncing from e3ti/4 to 1. Denote by y the curve representing the trajectory of the particle. Without evaluating the integral, show how we...
6. Let B(2) = i + 2z 4 - 2iz (a) Find the smallest positive real value M such that for every z on the closed unit disk D, |B() < M. [6] (b) A particle on the complex plane is trapped within a wall built along the unit circle. It travels from –i to e3ri/4 and then bouncing from e3vi/4 to 1. Denote by y the curve representing the trajectory of the particle. Without evaluating the integral, show how...
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