Find the four roots of z=1- jV3 (polar form only)

Q: Q4/ Determine the fifth roots of 2-j5 in polar coordinates.

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Q: Determine z° if z=- j. Leave your answer in polar form, 2 2.

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Q: Sketch the curve in the complex plane given by | Z-3| = | 7 + 3i } %3D i, z'+ 2?= 2. %3D

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Q: Q4/ Determine the fifth roots of 2– j5 in polar coordinates.

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Q: Find the polar coordinates, 0 ≤ θ < 2p and r ≥ 0, of thefollowing points given in Cartesian…

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Q: Evaluate into polar form 2-j7 3-j

A: Concept:  formula for a+ib in thepolar  form is rcosθ+isinθ  Here, θ=tan-1abr=a2+b2

Q: If Z1= −4+j8  ,  Z2= 8−j5  ,  Z3= 3−j7   and   Z4= −8−j9   determine i) Z = (Z1*Z2*Z3*Z4) /…

A: Given complex numbers are: Z1=-4+8jZ2=8-5jZ3=3-7jZ4=-8-9j These complex numbers are given in…

Q: Evaluate the by itercated integreal onverzting to polare coordinates. V16-n² 3nd ydn V16-パ 16-42 -4

A: This integration problem is solved by converting rectangular coordinate into polar coordinate

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

A: We  are given : f(z)=z4 f(z)=u+iv and z=x+iy ⇒u+iv=x+iy4 ⇒u+iv=(x4+y4-6x2y2)+i(4x3y-4xy3)On…

Q: The exponential polar form is

A: The exponential polar form is given by z=reiθ where r is the modulus of z and θ is the argument.

Q: Express in polar form: ej14 + 943 - (8-j6)/j²

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Q: Sketch the in the complex curve plane given by.- i) |2 -31 12+3i/ %3D

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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: Find the solution of polar coordinate f(z) = Z+ sine function by using Cauchy-Riemann method.

A: Cauchy Riemann method in polar form

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: Determine the fifth roots of 2 – j5 in polar coordinates.

A: To find the fifth roots of 2-5j

Q: 15, Зп /2) 3TT Convert the polar coordinates to rectangula rcoordinates (5, 3n/2).

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

A: Complex plane

Q: Find all solutions to a) z^4=i and b) w^3=8 using polar form

A: (a)

Q: SKetch the Cuove in the Complex Plane given by 12-3) = 1z+31| %3D

A: The detailed solution is as follows below:

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

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Q: If Z1= −4+j8  ,  Z2= 8−j5  ,  Z3= 3−j7   and   Z4= −8−j9   determine i) Z = (Z1*Z2*Z3*Z4) /…

A: Given data: The complex numbers are, Z1=-4+j8Z2=8-j5Z3=3-j7Z4=-8-j9

Q: What is the polar form of 7- j9 ?

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Q: Transform the vector C = cospâ – sinpô + cospsinp2 into spherical coordinates and then evaluate it…

A: Given cylindrical co-ordinates system as                                               we know that…

Q: II. Express in polar form: (a) 3+ j5. (b) -6+ j3. (c) -4 – j5.

A: For a complex number a+ib the polar form is given by rsin θ+rcosθ where, r=a2+b2 and θ=tan-1ba.

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

A: Cauchy Reimann eqaution: Let f(z)=u(x,y)+iv(x,y) be a function then  ∂u∂x=∂v∂y∂v∂x=-∂u∂y If the…

Q: 1. What is the polar form of (5-jl5) × (8+j6)?

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Q: find The unit Vectors tanent and normal to The ellipse x+2y= 6 at The Point (2,1).

A: Given, ellipse x^2+2y^2=6   point=(2,1)

Q: Find the parametric equation of the line through a parallel to b, using t as the parameter. 439 H 8…

A: We are given two vectors a and b  a=[-23], b=[-83] to find the equation of the line through a and…

Q: Determine in polar form the three roots of –27/2 + j27v2

A: We will find out the required roots.

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: Replace the Cartesian equations with equivalent polar equations and discusss its symmetries x2 + xy…

A: Given an equation in Cartesian form. We need to convert it into equivalent polar form and discuss…

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: Convert the Cartesian equation Z z = 6-√√36-x² - y² into spherical coordinates.

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Q: Express (1 – iv3) in the polar form, and show that: (1 – iv3)-2011 2-2012 (1 + V3i)

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Q: Find a parametric representation = z(t) for the upper half of = Z Iz – 4+ 2i| = 3.

A: Given to represent parametrically z=zt for the upper half of  z-4+2i=3 Let z=x+iy Then the equation…

Q: Find the quotient of z1 = -6+2i and z2 = 7+8i in polar form %3D %3D

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Q: polar Co-ovdina 4x²= y²-44+8

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Q: If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on Select one: х…

A: Given that: z=x+iyCurve: |z+1|=1

Q: Flnd the parametric equation of the line of ntersection of the planes and

A: First find normal vector then take cross product and use formula

Q: Express in polar form esin(-1+V3i). What are its arguments?

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Q: If 1+i 1. Compute and simplify the expression 5z2/(z+1) Do not use polar or exponential forms. Leave…

A: We have to simplify the given expression and draw the graph of the given expression

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

Q: Convert the followig into polar form,  2y=x-x3-xy2

A: The relation between cartesian coordinates x, y and polar coordinates r, θ is given by: x=r cosθ;…

Q: 1. Express in polar form, z =-4 + j2.

A: Since not a particular question asked as per guidelines solution to only first question(i.e Q1) is…