If Z1= −4+j8  ,  Z2= 8−j5  ,  Z3= 3−j7   and   Z4= −8−j9   determine i) Z = (Z1*Z2*Z3*Z4) / (Z1−Z2+Z3−Z4) ii) ln(Z2) in both Polar and Rectangular forms

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Q: 1. Use Cauchy- Reimann Equations to identify if it is differentiable or not, if yes then…

A: In the given question we have to check the differentiability of the given complex functions./…

Q: √4-j2 217 0/ convert the integral (SS Srdzr drdo) to rectangular coordinates and Spherical…

A: Here we can note that the given integral is in cylindrical coordinates. Also rectangular coordinates…

Q: Let f(Z) = y – 2xy + i(-x + x² – y²) + z² where Z = x + iy is a complex variable defined in the…

A: Solve by using Cauchy-Riemann equations

Q: osen y

A: Is it sen y =x

Q: 20) Find two sets f polar coordinetes, (r, o),0LOL2 IT Por the point (6,6) in recten- gular…

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Q: Consider the conic below x² + 4xy+ 4y² - 2/5x + V5y = 0 and determine what is asked. 1) Parameters…

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Q: 8. Find a parametric representation of the line through the point P(1,0,4) and perpendicular to the…

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Q: Q2\ If Z, =2+j, z, = -2+j4 and Z3 Z, -= - +- evaluate z3 in the form Z2 %3D x +jy and in polar form.

A: given z1=2+j , z2=-2+4j 1z3=1z1+1z2 evaluate z3 in the form x+jy and in polar form .

Q: II. Evaluate in rectangular form (a + jb) and in polar form (rz0) given: Z1 = -5 + j12,Z2 = 3 + j4,…

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Q: Question 7. Consider the solid in ryz-space, which contains all points (1, y, 2) whose z-coordinate…

A: Given, 0≤z≤4-x2-y2

Q: Express the functions ƒ(x, y) = (x2 + y2)5/2 and h(x, y) = x2 - y2 in polarcoordinates.

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Q: Transform (0, 5, 2) from rectangular into spherical form (here z is any negative number).

A: given rectangular coordinates is of the form (x, y, z) are (0,5,z) Now we are going to find…

Q: c) Use the polar form to prove that 2) (1+i/3)¬1° = 2-1'(-1+i/3) 2-"(-1+i/3)

A: We need to show that, 1+i3-10=2-11-1+i3. To show this, we are using polar form of complex numbers…

Q: Hw/ Express in both polar f rectamgular forms ;-234+j4I5] O (6+j5% Ans/ [476 219°25 ® (-16 -jq)"…

A: Handwriting solution

Q: 9.) Use spherical coordinates to evaluate 3/2 (x² + y² +2²) ³¹² dydzdx. 9-1² √√9-1²-₂² √√√9-x²-2²

A: To find the given integral using spherical co-ordinate system :-

Q: 2. Let r>o and Fo tina20 And use polar coordinates KZQ and use polar coordiinates (8,7) >(0,0)

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Q: i) Find the solution of Vu O in spherical co-ordinates.

A: The given Laplace's equation is,∇2u=0Now this equation can  be written as in the spherical…

Q: The parametric equation of the segment [AB] with A(1,0,5) and B(3,1,2) is: O x=1+2t y%3Dt z-5-3t -o<…

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Q: 2. Find the symmetric and parametric equations of the line containing the point A(1,2, 1) and x-2…

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Q: 9. Show that for a ± 0, the equation p = 2a sino cos 0 in spherical coordinates describes a sphere…

A: Given :  The equation ρ = 2 a sin ϕ  cosθ  .   To determine: The equation ρ = 2 a sin ϕ  cosθ  in…

Q: ») Shade the region in the complex plane defined by {rec: s |z+ 2+ 2i <1 4i E C

A: Complex plane

Q: Chapter 13, Section 13.7, Question 031 Find parametric equations for the tangent line to the curve…

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Q: For Exercises 27–30, determine whether the tests for symmetry in Table 7-2 detect symmetry with…

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

Q: i HW/ O change from. polar to Cartesian Co-ovdinate's (3, ) vE-2- Cose ... 1,0) © (-4, 3), @ (5,…

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Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

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Q: The parametric equation of the segment [AB] with A(1,0,5) and B(3,1,2) is: O x=1+3t y=t z=5+2t 0s…

A: Solution: Consider the given points are : A(1, 0, 5) and B(3, 1, 2) Parametric Equation of the given…

Q: .2 The surface z? = 1 is a 25 - - 36 hyperboloid of one sheet. Select one: OTrue OFalse

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Q: Give a parametric representation for the cylinder x^2+z^2=121

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Q: Find a parametric representation for the lower half of the ellipsoid 5x² + 4y2 + z² = 1.

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Q: Find the image of (2, –2) after a counterclockwise (passive) rotation of the axes about the origin…

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Q: Test for symmetry and graph polar equation

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Q: 1z2 in polar form. z1 = 5(cos(170)+i sin(170)) : z2 = (1/2) (cos(10)+i sin(10)

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Q: Describe the loci zz−2z−2z+8 = 0 expressed in terms of conjugate coordinates z, z.

A: It is given thatzz¯-2z-2z¯+8=0Where,z¯ is the conjugate co-ordinate of z.We have describe the locus.

Q: The scalar product equal (with philand phi 2 is orthonormal) lw> =i\@,> -2|@,> Ix> =3|0,>-2i|92>

A: given:  are normalized ,that is ..............................(1)

Q: What is the rectangular equivalence to the parametric equations? z (0) = 4 cos 0+2, y (0)=2 sin 0-5,…

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Q: If Z, = (-V3 + 3i), Z2 = (2+ 2i ) than 4 in polar form is : %3D Z2 Z1 5n 5n (cos +i sin 12 5n (cos…

A: z1=-3+3i,z2=2+2i,z1z2=-3+3i2+2iApply complex arithmetic rule:  a+bic+di = c-dia+bic-dic+di =…

Q: Suppose that f = u+ iv is analytic in a domain D. Show that the Cauchy-Riemann equations in polar…

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Q: What kind of conic section is given by the quadratic form ? -11x,? + 84x,x2 + 24x2? = 156 Transform…

A: Given quadratic form is-11x12+84x1x2+24x22=156The above conic is determined and transformed to…

Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

A: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

Q: Graph the lines and conic sections in Exercises 65–74. 65. r = 3 sec (0 – Ħ/3) 66. r = 4 sec (0 +…

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Q: Consider the conic below x² + 4xy+ 4y² – 2/5x + /5y = 0 and determine what is asked. Translation…

A: Here, the given equation is x2+4xy+4y2-25x+5y=0. Firstly, let's evaluate the angle of rotation, θ.…

Q: polar Co-ovdina 4x²= y²-44+8

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Q: Consider the conic below a2 + 4xy+4y² – 2/5x + V5y = 0 and determine what is asked. 1)…

A: If we have a rotated conic with the general equation: Ax2 + Bxy + Cx2 + Dx + Ey + F = 0, then, we…

Q: i need to convert below z=64-4*x^2-4*y^2 and above the xy-plane into polar coordinate however i am…

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Q: 3. If Å = +2.00m i - 3.00m k and = -4.00 mi - 3.00m k , find the resultant R = A-C using component…

A: Use the component method to find the difference of the vectors.…

Q: onto y %3D Find the projection of I =

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Q: 3. Transform x^2+y^2-2x+y-2=0 from rectangular to polar

A: The given rectangular equation is: x2+y2-2x+y-2=0