8. What is v–121+ 15 in the form a + bi? 0 + 4i 0 – 26i 15 – 11i O 15 + 11i

Q: -11-3,where z€C. Find z in a form a + bi. Given Z+1 A 13- 39i B. 1+ 31 C-1- D.1- 31

A: simplify for the value of z .

Q: 14.Let A= 3+2i 0 2 1+i 1-i B-( + ?) and B= Find AB.

A:

Q: Given z = -5+ 3i and z2 = 3 – 6i, express in the form a + bi %3D i. 4z1* – Z2 ii. Z2

A: Complex Cartesian form

Q: Prove that Eo 2i = 2n+1 – 1 - i3D0

A:

Q: 17. Given a = 4 – 4i and az = 4 + 3i, express %3D :11 in the form a + bi. a, az CLONE Dec 19

A:

Q: If Z= 3 – 2i and W = 4 – I, write  ZW in the form a + bi

A: Z=3-2i  &  W=4-i

Q: Find all solutions of cos2x + cosx = 0. + na, 3 + na, nK, wherenis an integer + 2nn, where n is an…

A: Simplification

Q: Let z=1+i√3 Calculate z6 using DeMoivre's Theorem Simplify and write your answer in the form a+bi,…

A:

Q: 1) Complete a proof of the following in 2 column form. Given: mz3 + mz8%3D 180 Prove: a I b

A:

Q: Show that 1/2 1+ 72 2 1. i%3D1 Xi n-1

A:

Q: O show that 2. I| a+ V 1= 11 + 1i if and only if ū. ů =0 %3D

A:

Q: Exercise 1: Given that Z1 = 1– 2i, z, =-3+ 4i. Find Z1 and express it in a+bi Z2 form. 2: 1 Given z1…

A: we are given some complex numbers. as per our guidelines we can answer only first question or first…

Q: 2.3 Use the Cauchy integral formulae to evaluate 22 - 1 Jo (9 – 2*)(2 + 2i))" where C is a circle |2…

A:

Q: Show that ri =1+i, r2 = 1-i is a solution of (3+ i)x + (1+ i)x2 = 4 +4i %3D

A:

Q: 13R Q2 Put the complex number Z = 2e in the "Cartesian" form Z a+ bi where a, b E R.

A:

Q: 1. Let z = 3+ 6i and w = a + bi where a, b e R. Without using a calculator, (a) determine , and…

A: Let's find ratio of given complex numbers.

Q: HW/ IF 2, = 1-3i, Zz=-2+si & Z3 = -3-4i determine as a+bi ,0 .0 z,-2.. 2;

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Given that: z, = 35445°, z2 = 24e3 and z3 = 10+11i. If 1z3 = a + bi, what is ? Note: Disregard the…

A: step 1:given thatz1=35∠450, z2=24e3i  , z3=10+11iand z14-z3z2=a+bifind…

Q: Solve the problem. 14) If u = -9i – 2j and v = -3i + 7j, find u V.

A: Let us consider two vectors u=ai+bj and v=ci+dj then u-v=(a-c)i + (b-d)j

Q: Find the imaginary component of In(2z + w) if z = 11 + 9i and w=10+4i .

A:

Q: 1. Given that z1 = 3 + i, z2 = 4 – 3i, z3 = -1+ 2i and z4 = -2 – 5i, find 21+z2 Z3Z4

A:

Q: Express each of the following in the form a + bi. 4. cosh(1 – i2)

A:

Q: 13. Find another representation 2, in which 3 a. ris negative and 0 < 0 < 2T; b. ris positive and…

A:

Q: Solve the following equations in Z6 with x expressed in both standard and non-standard names: (i) xx…

A:

Q: 1 1 u° +C = np " 18 (3t – 5)6 + C 18 9. (3t %3D

A: Consider the given integration as∫3t-45dt

Q: 2) × if it was 2+4i and 2=3-1 3+1 2+i 2 prove that x² + 3xy + y² = 6 =

A:

Q: 6. Express in a + bi form: 2i(i + 3)

A:

Q: If Z1 = 4 + 5i and Z 2 = -1 + I,  express in the form a + bi  (i) Z1 + Z2   (ii) Z1 – Z2

A: Formula used  sum of two complex number is given by  (a1+b1i)+(a2+b2i)=(a1+a2)+i(b1+b2)

Q: 8. a) Find in the form a + bi, where a and b are real, the values of Z for which 3 ii) Z 1 i) /zl=3…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Perform the required calculations and express your answer in the form a + bi. a) (1 + i )6 c) |3…

A:

Q: 6 7 /hat is [AB, the coordinates of A with respect to the standard [2 4 [o _0 1 1 asis B = of R2x2?…

A:

Q: Suppose a + bi ∈ Z[i] and c ∈ Z.Under what conditions is it true that c|(a+bi) (in Z[i])? Give…

A: Given that,

Q: Test the correctness of the statement * 2.1 * Isgn(-2.4)I + sgn(-0.2) = -2 TO * 2.2 + If x? x-y then…

A:

Q: (i) find gcd(2,3+5i) in Z[i], (ii) show that 3+4i and 4-3i are associates in Z[i] , do all , dont…

A: Solution (i)

Q: (5) Express ress the following in the form a+bi 3 (012 -0.41) ³ Ans: 0.016 i -0.088 +0. P

A:

Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

A:

Q: Find the value of S in (3A +4Si)(6-7i) = 3+5i

A:

Q: 4i then what is Re(

A: Given: z=3+4i. To find: Rezz¯.

Q: Find proj,u and scal,u by inspection without using formulas.

A: Given the graph

Q: Use DeMoivre's Theorem to find the following. Write your answer in standard form. V2 cis- 20 O…

A: Given (√2cos(9π/20))5

Q: 4. Let z = -4 + 3i and zw = -7 – 2i. By showing clear steps, find w in the form of %3D a+bi.

A:

Q: If z = 3 – 3i, express 5/z  in the form a + bi

A: The given value of z is z=3-3i.

Q: 1- Let z,=-5+11i and z3=2-21. Find in the form x+iy a) Re(1/2,) b) 1/ Re (z,) c) z,-z,? d) (z1/z2)

A:

Q: (2.5) Find another representation in which a. r is negative and °<0 < 2n. b. ris positive and -2n <0…

A:

Q: Let z, = 4 – 2i ; z2 = 3 + i ; z3 = 1 + 2i || -

A: Given z2 = 3+i and z3 = 1+2i

Q: Use z = a + bi to show that z + -z = 2a and z - -z = 2bi.

A:

Q: Compute the following powers and give your answer in the form a+bi (3 V3 3 = 0 2 2 | 123 = 0 1 V2 V2

A: Computer the powers.

Q: Show ther' 3 2

A:

Q: 19. Express in a + bi form: (5 – 6yi)(4 + 8i) – [(2 – 3yi) – 3(1+ 6i)]

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.