3.1. Express each of the following complex numbers in the form x+iy: (a). (V2 – i) – i(1 – v2i), (b). (2 – 3i)(-2+i), (c). (1 – i)(2 – i)(3 – i), 4+ 3i (d). 3 – 4i' 1+ 2i (f). 3 – 4i 2 - i 1+i (e). i 5i

Q: 3.4 Find the residue of f(2) = (1 – 2º) sin(1/2).

A: Find the residue of f(z)=(1-z^6)sin(1/z) We know that residue of f(z) is the coefficient of (1/z) in…

Q: 2.3 Evaluate the integral sinh 2 dz, 7 3i (z – 2i)4 2i 2+ 4 where C is the circle |z – 2i| = 4…

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Q: 5. Find the general solutions of the equations i) Zx - 4z,, – 5z, +10z, = cos(x+3y)-sin(x+3y) %3D

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

Q: 2) find the radius and coordinate center for the equation 2x42y+10y-12х-20-0 3) prove that sin 2x…

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Q: 27 1 1. The integral de can be converted into the following complex integral using a suitable…

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Q: If z = 2 ( cos 2¥/3 + isin 2¥/3 ), then z^3=   i. 2 - i8√3 ii. -4 + i4√3 iii.-8-i√2 iv. -8 - i4

A: Using de-moivre's formula :

Q: 21.2. Find the residue of f(2) = 1/ Cos z at all its poles.

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Q: Let z1 = 2(cos() + i sin 12 and z2 = 6(cos() + i sin). Find z1z2 and (Enter your answers in a + bi…

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Q: 3.12. Express the following in the form r(cos 0 +i sin 0), – T < 0 <T : (1 – i)(v3+ i) 4. 25 + 3 –…

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Q: 1) Prove that : [cos 0 – i sin 0] 2) For z = -4 + 4i , find z in exponension form. ||

A: Respected student, By the norms of Bartleby we are solving your first two questions, if you need a…

Q: Expand x?y + 3y – 2 in powers of x + 1 and y – 2. (up to third degree terms).

A: Given :- The given expansion x2y + 3y-2 in powers of x+1 and y-2.

Q: 3.27. Find a representation of the intersection of the cylinders = #, =1-2, that does not involve…

A: Given equations are x32=x1 →(1)x22=1-x1 →(2) Let us represent in figure,

Q: 7) Suppose a is a positive constant less than 7. Prove that the equation 2r+cos r = a has a real…

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Q: 24 dx J1- cos (8x) 24 dx J 1- cos (8x)

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Q: 2/2 16/1+cos 0 de 0

A: We use the half-angle identity

Q: 3 Find ALL solutions of cos 2x = 2 %3D

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Q: 1. Let n e N. Find all complex solutions to the equation: z" = i.

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Q: O Let n 3 be an integer. How many roots of the equation 2" + 3z +1 = 0 lie in the closed annulus {z…

A: We will use rouche's theorem.

Q: 3.4 Find the residue of f(2) = (1 – 26) sin(1/2).

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Q: 4) Exercie S Hst 2x+iy be a complex mumber such thet (-s(37)#0Then Re (tent3z))|c equal to: Sin Bx…

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Q: 9.1. Find all values of z such that (a). e = -2, (b). e² = 1+ v3i, (c). exp(2z – 1) = 1, (d). sin z…

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Q: 2) Use completing the square to find the following: s+4 а) L-1 ans: e-2t cos2t + e¬2tsin2t (s²+4S+8)…

A: We have to answer the following... a. L-1s+4s2+4s+8b. L-12ss2+12

Q: 11.1.5 Show that (a) cosx = Jo(x) +2(-1)" J2n (x), n=1 (b) sinx =2)(-1)" J2n+1(x). n=0

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Q: 4. Let z1 = 24(cos(75°) + i•sin(75°)) and z2 = 2(cos(15°) + i • sin(15°) ). Compute the %3D %3D…

A: SOLUTION-

Q: 1- 4cos*x = cos3x + 3cosx 2- Sin(In(i-i)) = 1 3- ((1+i)(1– i))' = (1+ i)'(1 – i)'

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find all values of the complex function of z for the e^(3z)=1z=x+iy

A: Its given that e3z = 1.  Given, z=x+iyWe need to sovle for z.

Q: Find all the roots of z²= - /3-j A z=2 (cos +j sin-) B z=/2 (cos (- =+ 2kn) +j sin ( 12 + 2kn)), 12…

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Q: 1. Convert the following expressions to its Julia equivalent. x+y² √√π-25) (a) e - cos' (2) sin³²…

A: We have to convert given expression to Julia equivalent. In Julia we have: a^b as ab exp(a) as ea…

Q: Example 1: Find length of the cardioid r = a(1 – cos 0) %3D | from 0 = 0,0 = 2n

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Q: Let z1 = 4 + 4i and z2 = 4 – 5i. Find (in the form x + iy): (5z1 + 4z2)? +i i i

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Q: 1+cos 2пу b. lim (2у-1)2 y – 2.

A: Given: limy→121+cos2πy(2y-1)2.

Q: (-n/6, 3) (지2, 3) (z16. -3) (37/6. –-3) From the graph, write the equation in the form f (x) = A…

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Q: 5) Evaluate the real integral 27T 1 de (5+ 3 cos 0)(13+5 cos 0) by complex variable methods, i.e.,…

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Q: Let A =5 [1-7i 1+ 4i] Find A* %3D 3i [1+7i l1- 4i -3il 51 5 (2) 4 30 [1-7i 1+4i 3il [1+7i 1-4i (c)…

A: We are given a matrix A of order (2×2), we need to find out A* (Transpose of matrix A) Transpose of…

Q: r(cos0+isin 0) with 0 (exact) in (0°,360°): а. z = 12-12i Z, =-3-3i z, =-4V3+ 4i b. с. Z3 = %3D

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Q: 3.4 Find the residue of f(2) = (1– :4) sin(1/2).

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Q: 3. у") - бу' () - 2у(t) %3 4 сos 2t- 4t3; у (0) — — 2,у'(0) — 3 4 cos 2t - 4t3; У (0) — — 2, у'(0) —…

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

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Q: 2. Solve: tan(3 T - 4) = 1 Te [0, 1 %3D 2 T = 80 %3D 10 3 A %3D 25 T = 20 %3D 3 л

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Q: 6. у %3D Gе" сos 3х + C,е* sin 3x

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Q: 4- Find e' in the form x+iy if z equals a) 2+ 1/2n i b) 0.5 -1.2i

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Q: 5. Find the general solutions of the equations i) Z - 4z, - 5z, +10z, = cos(x+3y)-sin(x+3y) %3D ii)…

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Q: 3 2 of a pizza in of a minute. Compute the unit rate by setting up a complex fraction and…

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Q: 2) S(3x + cos(x))[3x + 2sin(x) -312dx = A)13x +2sin(x)- 3 +C B)13x + 2sin(x)-31 +C C) other

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Q: Can i get help step by step?

A: Given integral is WE will use following substitution to evaluate the integral

Q: 2. Solve the IVP y(3) + y" = 5 cos(2.x), y(0) = 3, y'(7) = 1, y"(0) = 0

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Q: 4. Match each graph with its equation. (x – 2)² a. y = - (x-1)² x - 2 2. b. Y = x – 1 1. I – 2 54-3…

A: y=(x-2)2(x-1)2  1st option is correct answer.

Q: Compute z -20 where z is the complex number 6(cos 70° + i sin 70°). (i) 6²º(cos 40° + i sin 40°) 1…

A: To compute z-20 where z is the complex number 6cos 70°+i sin 70°.

Q: 3. у" — у' — 2у %3D5 sin x y(0) = 1, y'(0) = -1 -

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