Use De Moivre's Theorem to solve for z and leave your answer in polar form with the angle in radians (a) z = -8 (b) z* = -1+jv3

Q: Find z1z2 in polar form. 21 = 3 cos +i sin 22 = 4 +i sin ((늘)에

A: The objective is to find z1z2 in polar form.

Q: Q17:- In polar coordinates prove that** 第。

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Q: Write in Polar form: r(cosθ+isinθ)r(cosθ+isinθ). (0≤θ<2π0≤θ<2π and round to 3 decimal places)…

A: Given:     z = 8 + 10i    0≤θ&lt;2π

Q: Using the polar formula prove that?

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Q: 2. Convert the polar equation to rectangular coordinates. 1 r = 1+ sin 0

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Q: r = -4 sin 0,

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Q: Convert the equation rsin 0 = ln r + ln cos 0 from polar to cartesian.

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Q: polar curves intersect at right angles.

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Q: 12/2 Use polar coordinates to evaluate dydx.

A: The region is bounded by x=1,x=2,y=0 and y=x

Q: a) Reproduce the algebra required to convert this Cartesian equation to the polar form r = sin(20).…

A: Given the algebraic equation, (x2+y2)3=4x2y2 ⋯⋯(1) (a) Take x2+y2=r2, x=rcosθ, and y=rsinθ Then…

Q: 47. Show that every line that does not pass through the origin has a polar equation of the form sin…

A: Let's understand the relationship between polar coordinates and Cartesian coordinates. Please see…

Q: Find the points of horizontal and vertical tangency to the polar curve               r = 1 − sin

A: Consider the given polar curve: Here the objective is to find the point of horizontal and vertical…

Q: Find the angle α between the polar curves r1=eθ and r2=e−θ at the point of intersection.

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Q: Interior of r = 9 – sin 0 (above the polar axis) -

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Q: Find z1z2 in polar form. Z1 = 9 ( cos +i sin 22 = 6 +i sin 4

A: R eiθ=Rcos θ+i sinθ

Q: The polar equation 9 cos 0 + 2 sin 0 = X + 1 9x + 2y 1 9y + 2x = 1 9x + 2y = x² + y² || || 1 - r in…

A: To find  the cartesian form of the given polar equation.

Q: Find zw and z/w, Leave your answers in polar form.

A: Given the complex numbers  z=2(cos5π3+isin5π3)w=3(cosπ3+isinπ3)

Q: Find the polar equations of ALL the tangent lines to r = sin (30) at the origin.

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Q: True or False In the polar coordinates (r, θ), r can be negative.

A: Consider the following statement: " In Polar coordinates r,θ , r can be negative"  Determine the…

Q: 2. Use calculus to show that these polar curves intersect at right angles. = sin 0, r = cos 0

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Q: Express the polar coordinates 3, in Cartesian coordinates. ...

A: The solution is given below in the next step:

Q: Calculate the length of the polar curve r=1-sinθ on the given interval (0,2π).

A: In the given question we have to find the length of the polar curve on the interval . Concept:…

Q: Q2) Convert the polar function r = tan20 to cartesian. %3D

A: Let's find.

Q: Write in Polar form: r(cos 0 + i sin 0). (0 < 0 < 2n and round to 3 decimal places) – 12 – 3i r = ,…

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Q: Find polar coordinates of the point whose rectangular coordinates are (0, -4). Express u in radians.

A: Given: x,y≡0,-4 we know that polar coordinate for given rectangular coordinatex,y is given by r,θ…

Q: Show that every line that does not pass through the origin has a polar equation of the formr =…

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Q: 8. Convert the polar equation r =8 cos 0 into a rectangular equation.

A: we know     The formula  of polar to rectangular    r2 = x2  + y2  , where x = r cos( theta) and…

Q: find the area of the polar curve.   r=3-sin@

A: To calculate the area of the given polar curve , using integration

Q: A tangent at the pole to the polar curve r = is 2-4 sin 0 A 0 = = af pole usin6-2 Sing D 0=

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Q: find the quotient z1 / z2 in polar form where z1 and z2 are given below.  z = 24 [ cos ( 125° )] +…

A: We have to find polar form

Q: Express the 2D Cartesian  point P(5,10) in Polar coordinates

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Q: Replace the Cartesian equation with an equivalent polar equation. x2-y2=4 O cos2e - sin20 = 4 O r…

A: 1. x2-y2=42. r2=26r cosθ-6r sinθ-9

Q: Transform (0, y) from rectangular into polar form (here y is any negative number).

A: We have convert rectangular coordinates (0 , y) into polar coordinates: Where y is negative number-

Q: 5. Find the Cartesian form of the polar equation: r sin 0 = In(r cos 0)

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Q: Find the exact length of the polar curve. 3 sin(0), 0 < 0< 1/2

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Q: Convert the rectangular coordinates (4, 0) into polar form. Express the angle using radians in terms…

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Q: Find three additional polar representations of the point, using -2x < 0 < 2x. (Enter your answers in…

A: r = 3            a vector of length '3'. θ = -3π4  '-ve' : Rotate clockwise by 3π4…

Q: Express the polar equation r=2 sin 0 in cartesian coordirates.

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Q: Convert the polar equation r- 3 cosa 5 sin A in Cartesian equation form. )x² + y² - 3x = 5y 1- 3x =…

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Q: 1 r = sin 0-4 cos 0

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Q: Find z,z2 in polar form. 21 = 2 (co여(플) +i sin(플)); 22 =4( cos +i

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Q: 1 Sketch the curve r=-+sin0 cos 0 ,0 < 0<2n in the polar plane.

A: Any point on the Cartesian coordinate system is represented as x, y. Any point on the polar…

Q: 1. Convert the Cartesian coordinate (12,5) to polarcoordinate.

A: Given the cartesian co-ordinate(x,y)=(12,5)

Q: Express in true polar form, z = 5(cos 55° -j sin 55°)

A: We have to express in true polar form z=5cos55°-jsin55°.

Q: Plot the polar curve r=2(1–cos0) in interval

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Q: Find the area of the region. Interior of r = 4 + 3 sin 0 (below the polar axis)

A: Given that         r = 4 + 3 sin (theta) Here we have to find the area of the region below the polar…

Q: Find the polar equation for the Cartesian curve ² Or 1 T= cos 2 1 Or=sin @tan 0 2 T = Or= Or T = 1 1…

A: The given cartesian curve x2=y2 we have to find the polar equation

Q: Find the polar coordinates on the curve where the tangent line is vertical r=tantheta-1

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Q: find the prduct of Z1Z2 and the quotient of Z1/Z2. Express your answers in polar form.…

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