detailed solution for this one ????? 11. (a) Gi) If w=z+z-' prove that (i) z2 +...
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...
8. Let w cos(2π/5) + isin(2π/5). Here we describe how to express w in terms of square roots. (a) Show that w is a root of the polynomial 24+2+22+21. Hint: 25-1-(-(24+23+22+2+1) (b) Show that w + is a root of the polynomial u2 + u-1 (c) Show that Ve, where V5 means the positive square root of Hint: Figure out the sign of w by adding the polar forms of w and 1/w. (d) Put β--12vS So in part (c),...
Let z and w be non-zero complex numbers such that zw /=1. Prove that if z= z^(-1) and w=w^(-1),then (z + w)/(1+ zw) is real.I know z * z^(-1) = 1.
#4 (ii) Use (i) (otherwise no credit will be given!) to show that cos(20) = 2 cos - 1. 3. Prove that if z + is real, then z is real or |z| = 1. 4. Identify all the point in the complex plane which satisfy the following relations: (i) z2 = 2(2-1), 12-11 212 +11, (iii) z +11 <4 - 12 - 11.
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...
Please give a detailed explain of integration by parts and the induction to prove the equation. Thank you! Let Z1, Z2.. be a sequence of IID random variables with mean 0 and variance 1 and define i=1 and Another method of proof of CLT (the method of "moments") works by showing that for each m, the limit Lm exists, and the sequence satisfies the recurrence relation Use integration by parts to show that the sequence Rm variable, satisfies the same...
Please solve using the general solution method. Do not use Z-Transforms. 3.34. Consider the second-order homogeneous difference equation with initial conditions yl-1] pi and yl-2 P2. The coefficients a and a2 of the difference equation and the initial values p? and p2 are all real-valued, and will be left as parameters. a. Let z1 and 22 be the roots of the characteristic polynomial. On paper, solve the homogeneous difference equation for the three possibilities for the roots: 1. The roots...
step by step solution thanks alot BurAkEsEN. NAME: Q1. (30pts) Solve the quadratic equation z2(6 3i)z +6-8i 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(cos0+ i sin 0) of A and the 'first' root + isin 2 COS of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before...
Convolution Integrals. For part A the solution I got was t*exp(z*t) and for part B the solution I got was (exp(z2*t) - exp(z1*t))/(z2-z1). I need help with the third part of the question calculating (f * f)(t) without computing any integrals. f(t -s)g(s)ds by hand for (a) and (b) below Calculate (a) f(t) g(t) = et where z is a constant e21t and g(t) e22t where z1 and z2 are constants (b) f(t) Use your results from parts (a) and...
Problem 25 please -Sesin(2x)-9ecos(2x). 21. W = Span(B), where Br(x2e-4x , xe®, e-4x); f(x)--5x2r" + 2e-4-1e 22. W= Span(B),where B= ({x25, x5*, 5x)); f(x)--4x2 5x+9s5x-2(5x). 3 W Span(B), where B (Exsin(2x), xcos(2x), sin(2x), cos(2x)y): f(x) = 4x sin(2x) + 9x cos(20-5 sin(2x) + 8 cos(2x). 24, In Exercise 21 of Section 3.6, we constructed the matrix [D, of the derivative operator D on W- Span(B), where B e sin(bx), e" cos(bx)): Dls a a. Find [D 1g and [D'lg: Observe...