Describe by words and/or pictures, z, z1, z2, such that:
1) |z+5| = 3
2) -3 < Re(z) < 5
3) Arg(z1) = Arg(z2)
4) |z1| = |z2|
5) Im(z1 z*2) = 0
6) |z| = |z*| ** z* = "complex conjugate of z"
Describe by words and/or pictures, z, z1, z2, such that: 1) |z+5| = 3 2) -3...
Let Z! = 3H4, Z2-5-2, Z,--3-12, Z4--10-j6, and Z5--6-3. 1. Calculate Z1 + Z2 in rectangular form. 2. Calculate Z1 - Z2 in rectangular form. 3. Calculate Z3 + Z4 in polar form. 4. Calculate Za - Z5 in polar form. 5. Calculate Z1Z2-Z3 in rectangular form. 6. Find ZsZ7 in polar form. 7. Find Z7Zs in rectangular form. 8. Find ZsZs+Z7 in rectangular form Reduce the following to rectangular form. 10. Z1/Z2
Note: if z = (z1, z2, z3), then the vectors x = (−z2, z1, 0) and y = (−z3, 0, z1) are both orthogonal to z. Consider the plane P = H4 (1,−1,3) in R 3 . Find vectors w, x, y so that P = w + Span(x, y). Note: if z = (2,22,23), then the vectors x = (-22,21,0) and y = (-23,0,2) are both orthogonal to z. Consider the plane P = H(1,-1,3) in R3. Find vectors...
if z1=2+j, z2=3-j2, evaluate the following: If z,-2 +j, z2-3-j2, evaluate the following: 2z1 -z2 +3-j
Suppose z1, z2 and z3 are distinct points in the extended complex plane C ∗ . Show that the unique M¨obius transform taking these points to 1, 0,∞ in order is z → (z, z1, z2, z3), where (z, z1, z2, z3) is the cross ratio
Problem 1: Consider the following complex numbers: Z1 = 2 + j4 Z2 = 5e3 a) Write zi in polar form b) Write ze in rectangular form c) Plot the product of zı & z2 in the complex plane with x(0) = 0.3 Problem 2: Consider the system: dx/dt = -3x a) Solve the initial value problem b) Plot the resulting function
12. Suppose that fis analytic on a convex domain D and that Re(f ,(z)) > 0 for all z E D. Show that f is one-to-one on D. (Hint: /(z2) - sz) J,f'(w) dw, where is the line segment joining z1 to z2.) 12. Suppose that fis analytic on a convex domain D and that Re(f ,(z)) > 0 for all z E D. Show that f is one-to-one on D. (Hint: /(z2) - sz) J,f'(w) dw, where is the...
Al. Practice with complex numbers: Every complex number z can be written in the form z r + iy where r and y are real; we call r the real part of z, written Re z, and likewise y is the imaginary part of z, y - Im z We further define the compler conjugate of z aszT-iy a) Prove the following relations that hold for any complex numbers z, 21 and 22: 2i Re (2122)(Re z) (Re z2) -...
2. [1 point] Linear independence: a. Let x1=[1 2 3] , y1=[4 5 6] and z1=[5 7 9]. Are three of them independent? Show which MATLAB command(s) can be used to find out the answer. Also show the results of using the command(s). b. Repeat the process for x2=[1 0 3], y2=[4 5 6] and z2=[5 2 9].
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
and z2 = 1 1 + 3i 3-i a) Given that zı = find z such that z = 2 + i 4- ¿ 22 Give your answer in the form of a + bi. Hence, find the modulus and argument of z, such that -- < arg(2) < 7. (6 marks) b) Given w = = -32, i. express w in polar form. (1 marks) ii. find all the roots of 2b = -32 in the form of a...