. Let 21 2i and z2 = 1+v3i. (a) Express zi and z2 in mod-arg form. (b) Plot in the complex plane the points P, Q, R and S representing z1, 22, 21 + %2 and 21 22 respectively. (c) Find the exact values of: (i) arg(z1 + z2) (ii) arg(z1 – z2)

Q: Are the following two sets of coefficients orthogonal? -1, 0, 0, 1 -1, 1, 0, 0 Yes No

A: Given data is as follows: -1,0,0,1 -1,1,0,0 Yes the following sets of coefficients are orthogonal as…

Q: 6. Find all the roots of the following polynomials: a) p(r) = * - 3.r" +?+ 7x – 30 and b) p (r) = r*…

A: Note: Since we are allowed to solve one question at a time, we have solved the first one. Kindly…

Q: Find the conjugate of z = u+w If u = 6+2i,z= 1+4i

A: Step 1: The conjugate of a complex number z=a+bi is: zˉ=a−bi i.e., it is obtained by changing the…

Q: 1. Evaluate (a) (3+j2)+(5-j) and (b) (-2+j6)-(3-j2) and show the results on an Argand diagram. [(a)…

A: Given A pair of complex numbers as followsAimTo write the complex numbers in simplified form and…

Q: 6 -1 4 Compute A - 6I, and (6I3 )A, where A = - 5 2 -7 - 4 1 1 A- 613 =

A:

Q: Z2 in H = {0,4,8} find all left cosettes

A:

Q: Let p(z) be a polynomial with complex coefficiants and defree less than or equal to 2. It is true…

A: Given that, pz is a polynomial with complex coefficients and the degree less than or equal to 2. A.…

Q: Given the complex numbers z, = 2 + j0.51, zz = -0.4- j0.8, and z3 = 3+j3 find; |21Z2 (Z – 23) +…

A:

Q: Find the conjugate of z = -2 – 4i, and compute zz. z = zz =

A: Given that: z=-2-4i

Q: If 7,=-4-J5 Z2= -3 +j2, and Zg =2-3, what is Re (23-2 7, + 23 Note : z* is the complex conjugate Of…

A:

Q: 1 cartesian form of (9-3j)³ is 2.1047-j0.2266

A:

Q: Write z -5- iz + 3i in a+ bi form (x – y– 5) + i(3 – x – y)

A: To write z^(c) -5-iz+3i in the form of a+bi.

Q: Let A be a fixed constant positive number and f be an entire function with the property that |f (z)|…

A: We can come out with an answer by Liouville's Theorem, It states that a bounded holomorphic function…

Q: Write the following complex polynomials in factored form. You may check your final answer using…

A:

Q: Evaluate the complex numbers j(3 – j4)* (-1+ j6)(2 + j)² (a) z1 1 +j 4 – j8 11/2 (b) Z2

A:

Q: Suppose ū=i- j, v = −2i + 4j+3k and w = -5i + 4j. Compute the following values: |u| + |v|=| |-6u|…

A: Since you have posted a multi subparts question according to guidelines I will solve first(1,2,3)…

Q: Consider the matrices: 7 A = B = С — -6 6. D = [6 8 3], E = | 5 3 6. -6 3 F =| 3 9 G = 3 -3 5 3 7 5

A: In this question given that any type of metrix and help of these metrix we find the value of any…

Q: if complex numbers Z1= 4.5-j5.1 , Z2= 3.2- j6.2, Z3= 2.25-j5.6 , Z4= 7.5-j9.2 , then calculate…

A: Given complex numbers are…

Q: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1 – j2), j 2- j3 1 +…

A:

Q: nd a, b e R such that 4 5 a + bi 1- 2i i - 2 i- 2

A:

Q: Let z2T3-L p=S+Si O fird all the complex mumbers %3D guien by hza

A:

Q: 2. Let k be a complex number and P(x) = 8x³ − 4kx² + (2k+6)x +3. Find all values of k for which P(x)…

A: Given the polynomial  P(x)=8x3−4kx2+(2k+6)x+3 , we need to determine the value(s) of  k  such that…

Q: 2. [(x – 1) + 5][(x – 1) – 51]. Write the answer in the standard form

A: To write in standard form.

Q: Find the distance d (in the complex plane) between z = 2 + 7i and w = 11 - 10 i. d = √ (1)² + (9)² X

A:

Q: How many solutions does Ax = [1]   have?

A:

Q: z3-22 If z = -4 - j5, z2 = -3+ j2, and z3 = 2- j3 , what is Re ( Note: 2* is the complex conjugate…

A: Given  z1=-4-j5 , z2=-3+j2 & z3=2-j3 We have to find Rez3-z2z1+z3*   where z* is the complex…

Q: 2+ i 4 – 2i Find the conjugate transpose of A = -1— 3і 3 — 51. Ex: 1+ 2i A*

A:

Q: Answers to 4.5.2 Solving Polynomials: Irational Conjugates 1) 1- V7, 2-2vi 2) -3 - Vi, 3- VE 5) flz)…

A: