Given that z1 = 6−3 i and z2 = 3−11 i, find the following in the form x + y i
_
Z1 =
_
Z1 Z2 =
Z1/Z2=
Given that z1 = 6−3 i and z2 = 3−11 i, find the following in the form x + y i _ Z1 = _ Z1 Z2 = Z1/Z2=
10p Find complex numbers t = Z1 + Z2 and s-Z1-72, both in polar form, for each of the following pairs 3, b. Z1 3<30° and Z2 3-150
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...
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
Use z1=4(cos7π/12 + i sin7π/12) z2=9(cos5π/12 + i sin5π/12) a) Find z1z2. Leave in polar form b) Find z1/z2. Leave in polar form.
4 points) Let Z1,Z2,...,Z1 be 11 independent N(O, 1) variables, and let Provide answers to the following to two decimal places Part a) Evaluate the moment generating function Mz2 (t) of Z2 at the point 0.23 Part b) Evaluate the moment generating function My(t) of Y at the point t = 0.31 . Part c) Find the mean of Y. Part d) Find the variance of Y.
Express the product of 21 and 22 in standard form given that: z1 = 14 (cos(x) + i sin(a)] and z2 = 2/2 (cos(3) + i sin(*)] 23.275 - 32.035 32.035 - 23.275i 32.035 +23.275i • 23.275 + 32.035i
Write 21 and 22 in polar form. 21 = 5 + 5i, z2 = 16 Z1 = x 22 = x Find the product 2122 and the quotients 1 and 1 (Express your answers in polar form.) Z2 2122 x 21 22 1 21 = X
if z1=2+j, z2=3-j2, evaluate the following: If z,-2 +j, z2-3-j2, evaluate the following: 2z1 -z2 +3-j
Question 1 Let Y = 1 +2X + u where X = Zn4Z2, u = Z1-22, Z1 and Z2 are independent standard normals. We have iid observations (X,, Y1 from this model. (a) Suppose we run the following regression to obtain the OLS estimator β0Ls. What would you expect the value of β0LS to be when no Please give a numerical answer (b) Suppose we run the following regression to obtain the OLS estimator γ0Ls. What would you expect the...
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"