if z1=2+j, z2=3-j2, evaluate the following:
if z1=2+j, z2=3-j2, evaluate the following: If z,-2 +j, z2-3-j2, evaluate the following: 2z1 -z2 +3-j
Alength-13Type1real-coefficientFIRfilterhasthefollowingzeros: z1 = 0.8,z2 = −j,z3 = 2−j2, z4 = −0.5 + j0.3. (a) Determine the locations of the remaining zeros. (b) What is the transfer function H(z) of the filter? (Hint: Use matlab function poly to determine the transfer function.)
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"
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
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=
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...
9The middle area between z1 and z2 is 0.7500 P(z1<z<z2) - 0.7500 1.04 1.08 1.15 1.04 1.08 1.15 1.20 10 The middle area between z1 and z2 is 0.8000 P(z1<z<z2) - 0.8000 1.28 1.34 1.41 1.48 1.34 1.41
| Assume that Z1 and Z2 are two independent random variables that follow the standard normal dist ribution N(0,1), so that each of them has the density 1 (z) ooz< oo. e '2т X2 X2+Y2 Let X 212,Y 2Z1 2Z2, S X2Y2, and R (a) Please find the joint density of (Z1, Z2). (b) From (a), please find the joint density of (X,Y) (c) From (b), please find the marginal densit ies of X and Y. (d) From (b) and...
Problem 2. (Conditional Distribution of MVN) Let Z1, Z2, Z3 be i.i.d. N(0,1) dis- tributed random variables, and set X1 = 21 – Z3 X2 = 2Z1 + Z2 – 223 X3 = -221 +3Z3 1) What distribution does X = (X1, X2, X3)T follow? Specific the parameters. 2) Find out P(X2 > 0|X1 + X3 = 0).
Using complex or magnitude angle math to solve for Z, V or I Let Z1 = (2 + j2) Zg = (1 + j2) Zg = (4 + j2) 11 = (4 + j2) Solve for A) Zi + Za + Zs (Series impedances) B) Zi ll Z2三? (Parallel impedances) C) Il * Z3-) (Ohms Law) D) Vı/Zs-? (Ohms Law)
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...