Let u = 6i – 5j, and w = -i-2j. Find ||w- ul. |w-ul (Type an exact answer, using radicals as needed.)

Q: Q: For any two complex numbers z, and zz, prove that z-z|+|z+!z|=z-z-2+z-z+

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Q: Write a in the form a = a-T+anN at the given value of t without finding T and N. r(t) = (3t + 3)i +…

A: r(t)=(3t+3)i+(-2t)j+(3t2)k,t=-1 Differentiate to get velocity, v(t)=3i+(-2)j+(6t)k Find magnitude…

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: The complex numbers an, n > 0, are defined by the condition that Σan (z-2i)" = 1+ 2z+3z² + Σ(n+1)z"…

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Q: Write a in the form a = a-T+anN at the given value of t without finding T and N. %3D r(t) = (- 2t +…

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Q: Write a in the form a = a-T+anN at the given value of t without finding T and N. 2, r(t) = (– 3t +…

A: aT=ddtv(t)  and  aN=a(t)2-aT2

Q: Derive the canonical form of the given parabolic PDE (b) - 3u. +64.- 3u = cos(x).

A: given 2nd order PDE -3uxx+6uxv-3uyy=cosx   ...i claim- to derive the canonical form of given PDE

Q: 4. Consider the complex number w = 3cis (). For which value(s) of k is z - w a factor of the…

A: We will use remainder theorem to find the value of k. Remainder theorem says that if x-a is a factor…

Q: express z1z2 and z1/z2 in the form a+ib. Q. z1 =1+i, z2 =3+2i.

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Q: Prove that there is no complex number z such that 1 |z|«anda,z' = 1, where|a,| < 2. 3 r=1

A: In this question we have to prove that there is no complex number z such that z&lt;13 and ∑r=1n…

Q: Give algebraic proofs of properties (1)u + (-u) = 0 ,(2) (c + d)u = cu+ du

A: Let be a vector such that  Multiply  with -1. Adding the two results,  Thus,is the additive…

Q: 4. Find the harmonic conjugate of u where u(x, y) = x2 – y? – 2xy – 2x + 3y.

A: We will answer the first question since exact one was not specified, Please resubmit the question…

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 -…

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Q: Given that z, = -3 +i and z, = 4 + 4j. Find the modulus and argument of Hence, express in polar…

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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…

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

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Q: Find all the numbers z such that e^2iz= 5i.

A: We are given : e2iz=5i Now Using  Euler's equation: ( eix=cos x+i sinx) ⇒e2iz=cos (2z) +i sin(2z)…

Q: Find the conjugate of z if z = (1+ 3i) + (-2-4i) O -1+i O-1-i 01+i 01- i

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Q: ez = -2

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Q: baphress -4i in esponenial form reio the Qunge OLOC2TI in

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

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Q: Let z1 = 2 – 3i , z2 = -1+ 5i , and z3 = -6- 2i. %3D 2123 Evaluate: z2 . Express final answer in…

A: The given complex numbers are z1=2-3i, z2=-1+5i and z3=-6-2i The addition  and subtraction of two…

Q: D dz |z|=1 |z-a|² 2

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Q: express z1z2 and (z1/z2) in the form a+ib z1=-1+3i, z2=2-i

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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: Write a in the form a = a- T+ anN at the given value of t without finding T and N. r(t) = (t + 5)i +…

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Q: Find the sum of f(i) = 2i +2 over the integers 1, 2, 3, ..., 20.

A: Given,           The sum of fi=2i+2 over the integers 1,2,3,...,20

Q: Find A'A and AA". -1 1 4 A = 2 0 2 (a) ATA (Б) ААТ Which of the products are symmetric? (Select all…

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Q: Find the projection of b = 5i – k onto à = i+ 2j+ 3k. %3D

A: We have to find the projection of →b on →a

Q: Q[V2 ]is Principal Ideal Domain..

A: Q[√2] is Principal Ideal Domain. True.

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

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Q: If Z=1//2+j/v2 then the value * ?=of conjugate of Z^5

A: According to Euler, the complex number of the form cosθ+isinθ can be written as eiθ. The conjugate…

Q: Determine whether = e', y2 = sin2t, y3- cos2t make up a fundamental set of solutions by finding the…

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Q: Find the source Q cx) Such that the So lutiim Uckit) of + Q(x) 2 ə x² 0 < x <∞ | U(x,o) = 0

A: given equation ∂u∂t=k∂2u∂x2+Qx ,       -∞&lt;x&lt;∞            ...iux,0=0 claim- find the source Qx…

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

A: The given value of z is z=3-3i.

Q: express z1z2 and z1/z2 in the form a+ib. Q. z1 =4−i, z2 =1+3i

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Q: Determine all solutions u = u(x1, x2) of du du (1 — и). + (1+u) dx1 = 1, dx2 X1, X2 E R, u(x1, x2) =…

A: Determine :- The solutions of u = ux1 , x2 of  1-u ∂u∂x1 + 1+u ∂u∂x2 =1     x1 ,x2 ∈ℝ, ux1 , x2 =0…

Q: Prove that the function w(z), expressing the roots of the equa- tion 3ర్ - 25w° + 60u - 2 = 0 in…

A: We consider z as a parameter and for each complex value of z will look for all complex roots w of…

Q: Write a in the form a = a-T+ anN at the given value of t without finding T and N. %3D r(t) = (212)…

A: Here I am attaching image so that you understand each and every step.

Q: Show that, for any complex number z, zz = |2|², z+z = 2Re(z) and Re(z) < |z|. Henc show that i. [21…

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Q: For all complex numbers Z1,Z, prove that |2z|+|*z|s]°z+z[

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Q: express z1z2 and z1/z2 in the form a+ib. Q. z1 =− 1+3i, z2 =2−i.

A: Now,

Q: a) Check that the functions e^x, e^-x,coshx are solutions of y'''-y'=0 b) show directly that…

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Q: Z Is any complex number interior to any simple closed contour dz 2 Ti, n= 1 prove that for all…

A: It can be solved using cauchy integral formula

Q: A space ship travels at 25 miles per hour and traveled continuously for 211 hours. 4 Enter the…

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Q: What is the polar form of (2+ j3) x (4- j5)? O 23.09/31.3° 23.09/5.0° O 19.2545.0° O 19.25Z31.3°

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Q: a) Show that u(x,y) = x3 – 3xy2 + 3x2 – 3y2 is harmonic and find its harmonic conjugate

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Q: (d) Prove that IJ CINJ. Give an example where 1JÇINJ. (e) Is (ab a e 1,beJ} an ideal in R?

A: ANSWER :

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.