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

Q: Suppose z = x + 2i and u= 3+ yi where x, y E R. Find the smallest positive value of x z + u for…

A: Substituting z=x+2i and u=3+yi in z+uz-u:  z+uz-u=x+2i+3+yix+2i-3+yi           =x+3+2+yix-3+2-yi

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: if x~unif. (0,2),find the U.b. of p(lx - mul>= 2)

A: Given X~Unif(0,2) Result: if X~unif(a,b) then  Mean=(a+b)/2 Variance=(b-a)2/12

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

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

A: Z=3-2i  &  W=4-i

Q: 8. Solve the following IBVP: U = u + sin(3nr), 00, u(0, t) = u(1, t) = 0, t20, u(r,0) = sin(72),…

A: Given ut=uxx+sin(3πx), 0<x<1, t>0u(0,t)=u(1,t)=0, t≥0,u(x,0)=sin(πx), 0≤x≤1

Q: If x=sin@,y=0 ,y=cosp0,Prove that (1-x²)y,-xy,+p°y=0

A: Given, x=sinθy=cospθ Required to prove, 1-x2y2-xy1+p2y=0...1 Then finding dydx by using chain rule,…

Q: If y = exp(-x²) show that -2xy and hence prove that, for n > 1, %3D y(n+1) + 2xy(") + 2ny("-1) = 0.…

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Q: Use symmetry to evaluate the followingintegrals.

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Q: Solve the following forr W=4xc for c %3D C = (Type an exact

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Q: ) Compute the four 4th roots of −T + Ti where T=7

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Q: Solve the Auxiliary DE 75. и"" + u" — 2и 3D 0

A: Note: - “Since you have asked multiple question, we will solve the first question for you. If you…

Q: Q6:-Prove that: y" = 1 if y=;csc (tan"

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Q: Given z = 3– 4i and w = -1- 2i, compute the following and express your final answers in the fe-n a +…

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Q: у" + Зу" + Зу' +у%3D0

A: We have to solve the differential equations

Q: 2) Show that (1 – x²)P",(x)P'm(x) dx: 21(l + 1) Sim• 21 + 1

A: Given:-  ∫-11(1-x2) p'l(x)p'm(x)dx=2l(l+1)2l+1δlm

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: Consider 7(t) = (2t³ – 2, 3e“, – 2 sin(3t)). Find Don't include the +C. %3D

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Q: ez = -2

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Q: for z = In(2® + y*). Find

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Q: %3D Bi'

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Q: S Prove that L(cos 3t) (s²+9)

A: Given L(cos3t)

Q: Use the substitution x = et, to solve the following Cauchy-Euler equation: x²y// – 4xy/ + 4y = x³ In…

A: We will find out the required solution for given Cauchy Euler differential equation.

Q: 1 Assume that 1 < a < b_and equation is solvable. + x = Show that this * – b'

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Q: Let 7(t) : - Find (don't include the +C) V

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Q: Find all the values of x in the interval [0,2pi], that satisfy the question.  10cos(x)+5sin(2x)=0

A: Given equation is Solve the given equation for x

Q: 57. Use the substitution u = x/3 to prove dx 1942=tan 1+0 www C 9+x² 3 3

A:

Q: if क f z₁ = 2 ( 65 30 +isin 30) and Z₁ = (Cos60 +isin60), Find the following Z₁ * Z₁ له الله چه

A: Here we have z1=2cos30°+isin30° and z2=13cos60°+isin60° We have to find 1) z1·z2 and 2) z2z1

Q: he coefficient ao of Fou +2 t. く?

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Q: the following DE are Bernouli type and solve: 1. y’ – x = y 2. y’ + 5y/x = x 7 y 4

A:

Q: 28. IfI:zxzr = 0, ris a. positive b. negative с. zero d. impossible to determine from the…

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

Q: 2ху 3. y' = -x?

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Q: 2-If w(x, t) = Sin(x - + 3t) + Cos(2x+ 6t), prove that wtt = 9wxx %3D %3D

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Q: 7. a) Prove that for r > 0 * (E) + c. Vr2 – r²dx = vr² – x² + -1 sin 2 +C.

A: To prove: ∫r2-x2dx=x2r2-x2+r22sin-1xr+C

Q: Suppose T(z) = Find a solution to T(x) = | %3! in terms of z. Note: We are using T : C → R? such…

A: The function T is defined from complex plane to cartesian plane. T(a+bi)=a-b0.  Given the line in…

Q: Express the answer of the following problems in form rciso with and -Tss下 O Z: I+i 1-i3

A:

Q: -3 [-1+v3i]

A: Explanation of the answer is as follows

Q: 1. Given A= For which value(s) of a and b will A be singular?

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

Q: - Show that u(x,t) e-a't[A sin(2x) + B cos(Ax)] satisfies the PDE uz = a?uxx for arbitrary A, B and…

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Q: FIND THE UNTQUE SOLUTION OF AU= 0 34/x1<4 SUCH THAT U(x) 5 on x =3, U(x)=6 on /×/ =4 on 2 in R in R…

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Q: 2.18 Obtain the canonical form for the following elliptic PDES: a?u a?u (a) ax? дх ду ay? a?u a?u du…

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Q: 3 and ajj = i. j. Th

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Q: Express Q(x) = cos4 (x )+ 12 as the composition of three func-tions; that is, identify f, g, and h…

A: Q(x) = cos4 (x )+ 12 We need to express the given function as a composition of three functions  that…

Q: Compute for the value of tanh-(1 – i) In 5 my + 2.13i In /2 + 2.13i Inv - 4.25i 2 In /2 + 2.13i

A: Let, tanh-11-i=z. Thus, solve for z:…

Q: a. Let z1 = 2 – 3i, z2 = 3 + 4i and z3 = 1– V3i. Find z1z2 + z3 then sketch it on Argand diagram.

A: Simplify Z1Z2 + Z3 in simplest form and convert it into polar co-ordinates.

Q: Find the exact values of s in the given interval that satisfy the given condition. [0, 2n); cos s=-

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Q: If the coordinates of any two points ₁ and ₂ are (x₁, y₁) and (x2, ₂), respectively, then prove that…

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Q: 2. find the the following equation in simplest arbi Saution set of form. X-3x + 9 = 5Y-10

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Q: 3. 1+x2 хр xp q Find b such that J Tuy2

A: By using integration formula we can find the value of 'b'. See attached for detailed solution.