18. Let z be a complex number satisfying 12|:|* = 2|z + 2|² + |z² + 1]² + 31. What is the value of z + clear (B)-1 (C)를 (D) 1 (E) 4 (A) –2 00

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

A:

Q: If z1,72,., are complex numbers such that = =.==,| =1,Prove that 1. 1 1

A:

Q: 1) Prove that there are no positive integer solutions to the equation x2-y?=1

A:

Q: 3. Use De Moivre's Theorem to solve for the roots of : a® – 1 - j1 = 0 O A. 1 cjs (T/24 + rtk) ; k =…

A: Introduction: DeMoivre's theorem is a significant theorem in complex analysis. It is used to find…

Q: 1-z+2 dr +10+9 Use the Residue theorem to evaluate

A: The integral is I=∫-∞∞x2-x+2x4+10x2+9dx. Consider fz=z2-z+2z4+10z2+9 By theorem, if a > 1 and M…

Q: (1) Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute…

A: First let xy be positive  Then either both x and y are positive or both are negative  If both are…

Q: Prove that x4+4=(x+1+i)(x+1-i)(x-1-i)

A:

Q: 86. Show that Z, = r(cose + isine) and Z2 = r[cos(-6) + isin(-6)] are conjugates. %3!

A: Given,

Q: Vhich among thế chôičes satist etters only. 2а. у" - Зу'- 10у %3D0 Co-5x C o2x

A:

Q: φι dz (z-zo)" [2πί το n = 1 n>1

A:

Q: 1-Show that У +їх ave X + iy =/=1 where Complex numbers ? X+iy and

A:

Q: Evaluate the integral. 2 (3u - 5)(u + 2) du -1

A:

Q: 2. Find the general value of z in the complex number : - jl O A. J[(2/3)nk+ Tt/6] O B. J[(2/3)nk -…

A:

Q: Prove that (3-2)(x+2) = 3+2i ifitues.

A:

Q: 6. Show that when ) < |z - 1| < 2, e - ( - 3) (2 - 1)(2 – 3) Complex Analysis n=0 (z-1)" 2+2 2(z-1)

A: We use Laurent series to prove given example.

Q: 4. Prove that 3i² + i = n(n+ 1)?

A:

Q: Q4: 1- Prove that (1-0+(1+ () 0. 2. Put in the form a+ib ((1+i))- ((1-i)).

A: Here we have to prove that, 1) 1-i2+(1+i)2=0 2) Put in the form of a+ib, 1+i22-1-i22

Q: 2. Let K be a finite simplicial complex and n is equal to the number of path-connected components of…

A: For simplicity, here we use r, instead of n.

Q: (9) Is an complex annullus Ann(2o, R1, R2) with 0 < R1 < R2 simple connected?

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: 3V Show that there dã do not exist two real numnbers which add to 7 and multiply to 13. It is not…

A: our objective is to conclude the result

Q: (b) Show that 1+ 2/2 has infinite order in R*.

A: Given that R=m+n2 | m,n∈ℤ (b) The objective is to show that 1+22 has infinite order in ℝ×

Q: Prove that the equation x+5x=4cosx cannot have more than one real ro

A:

Q: (10') Use Rouche's theorem to find the number of roots of 2z4 – 5z + 1 = 0 (1) for |z| < 1 (2) for…

A:

Q: 6. Show that when 0 < |-1|< 2, (z-1)(z-3) Complex Analysis (z-1)" 2+2 =-36 z−3) ² A=0 2(z-1)

A: We use substitution and Laurent series expansion.

Q: f for ƒ : R - {2} → R- { 5} indicated by f (x) =(5x +1)/(x -2a), a bijection can be made from [0, 1)…

A: Bijective function: The domain is set A and the co-domain in set B relates elements of two sets A…

Q: For complex number z and w, prove that zw-wz=z - w if and only if z =w or, zw = 1.

A: We know that , for a complex number|z|2=zz¯and when z is a real numberz=z¯

Q: 13 3. Use the IVT to prove that y = r Inr has at least one zero on 2 2

A: Above function is continuous function in given interval. So we can apply IVT

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

A:

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

A:

Q: Hi, there are two questions a) and b) attached  Thanks so Much!!!!

A: Given that z is a complex number satisfying |2z – 1| = |z – 2|. We need to prove that |z| = 1 by two…

Q: Theorem 4.8.1 Irrationality of V2 V2 is irrational.

A: For any integer n such that n² is even then n is also even.

Q: Use Bombelli’s approach to find a complex number c = a + bi such that c3= 18 + 26i where a and b are…

A:

Q: How can we prove to get dual from primal standard form? from this primal standard form Max.z = c'x…

A:

Q: 22. Given that Z= 2-3i, express Z/Z* and Z(cos-- isin -) in the form a + bi, where a and b are real…

A: Note: "Since you have asked two questions, we will solve the first question for you. If you want any…

Q: What is the midpoint between z1 = 9i and z2 = 4? (2, 4.5) (-4,-9) (-2,-4.5) (4, 9)

A:

Q: Question is attached, Thankyou

A: Let us take z = x + iy.

Q: 2.2.12 Prove that if x and y positive real numbers, then Vx+y # Vx+ Vy. Argue by contradiction. are

A: Let x and y are positive real numbers. Also let x+y=x+y Now squaring on both side,we get…

Q: Prove that |z₁+z₂²2 = |z₁|² + 12₂², if z₁/z₂ is purely imaginary.

A:

Q: 2. Solve for the complex mumber z in r (4+ 36) – 7 = 7x - 4zi. Show all algebra.

A: Given expression is x(4 + 3i) - 7 = 7x - 4xi

Q: How can I find all monic divisors of degree 1 in Z_7 [x], 5x^2+5x+4? please help me get started with…

A: Set of all Polynomials over a field ℤ7 is given by ℤ7x=anxn+an-1xn-1+ . . . +a1x+a0  where a0,a1, .…

Q: Let z be a non-zero complex number. D if OsArg(z)sTt/2 D for all complex numbers D if OsArg(z)sn…

A: we know that logzn≠nlogz for all complex numbers. Since ew=z and -π&lt;Imw≤π If w=logz, nw is a…

Q: or complex number z and w, prove that zf w-|wfz=z-wif and onlyif z = w or, zw = 1. W

A:

Q: Q4: 1- Prove that (1– i)? + (1+ i)² = 0 . %3D 2- Put in the form a + ib ((1+ i)²)² - ((1- i)²)².

A:

Q: 5. Compute for the product of the complex coardinates :(3, 1)(3, - 1) a. (2,1) b. (1,1) c. (3,1) d.…

A: The given problem is to find the product of the given complex coordinates, We have to use product of…

Q: Prove that JI = J [1 0 0] I = |0 1 0 Lo 0 -1 2 -31 J = 4 5 -6 %3D –7 8 -9 1.

A: Considering the matrix multiplication of J and I

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

A:

Q: 5. Evaluate the integral JI. dA, R = [-2, 4] × [1, 3]. R

A:

Q: 7.1) 19) Evaluate the integral.

A:

Q: #02:-Discuss all the cases of reducible to hamggenou D.E form.

A:

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

A: