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

Q: 5. Convert the given functions into the desired coordinates. (a) 2x-5x³=1+xy into polar coordinates,…

A: Solution of this question is :

Q: Use the identity cos 20 = cos² 0 – sin² 0 to find a polar equation of the hyperbola x² – y² = 1.

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Q: Write a polar equation of the form r sin(0 – 0,) = ro for the line 2/3 x+2y = 1. %3D

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Q: Find a polar equation for x? + y² = 2

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Q: 5. Solve the following and leave your answer in polar form. V22? = -Z - V2 %3D

A: Put z=a+ib

Q: The polar equation 9 cos 0 +2 sin0 = in Cartesian form is defined by I Y A. C. 9x +2y=1 +/-/22 - 1 9…

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Q: Use the identity cos 2θ = cos2 θ − sin2 θ to find a polar equation of the hyperbola x2 − y2 = 1.

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Q: Find the exact length of the polar curve r=1+ cos 0

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Q: Find a polar equation in the form r cos (θ - θ0) = r0 for each of thelines y = -5

A: We need to find the equation in polar form for the given line

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

A: R eiθ=Rcos θ+i sinθ

Q: 9. Transform the equation 2x?+2y?3 into a equa tion. Polar

A: Given

Q: Convert the Cartesian equation x² + y² -2x= 0 to a polar equation. x2 + y2 -2x 0= O 2=-2 cos e Or= 2…

A: Given artesian equation,x2+y2-2x=0Put…

Q: Show that the polar equation for x2/a2 + y2/b2 = 1 is                                           r2 =…

A: Plug x=rcosθ and y=rsinθ

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: 10 Convert the Cartesian equation 2 xy = 1 in polar equation form. r²cos2θ = 0 cosθsinθ = 1/2…

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Q: 14. Restate -4x = -5y in polar form. Present your answer solved for r.

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Q: Replace the Cartesian equation x² + y² equation. OA) r sin² 0 = 4 cos 0 B) r = 4 sin 0 Oc) r = 4 cos…

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Q: 5. Consider the point with rectangular coordinates (1, – V3 ). sState the coordinates of the point…

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Q: Write a polar equation of the form r sin(0-00) = ro for the line 3 x + y 1. 2mark dentify and draw…

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Q: 2. Transform the polar equation into a Cartesian equation. 4 r = 4 + sin 0

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Q: Find 1 in polar form. Z2 -BV5 (cos(T)+i sin(m); 22 = V cos +i sin

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Q: #7. Convert into polar equation form. ( 4 marks each ) a) y=5x+3

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Q: (4430°)-(24225°) d. (24140°)(34300°) (Express your answer in polar form)

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Q: = Replace the polar equation 8r cos 0 + 9r sin 0 Cartesian equation. OA) 8x +9y = 1 B) 8y + 9x = 1…

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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: 2. Represent z = 3 – 3i in polar form.

A: As we know that; The polar form for the complex number z=x+iy is: z=rcosθ+isinθ  .....(1) Where;…

Q: Convert the Cartesian equation x 2 + y 2 - 6x = 0 to a polar equation.  r² = 6cosθ r = 6sinθ r =…

A: The given Cartesian equation x 2 + y 2 - 6x = 0 ................................... (1)

Q: 8 Convert the polar equation r 2 = -2 sin 2θ to a Cartesian equation. x2 + y2 = 2 xy ( x2 + y2) 2…

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Q: Find the equation of the line tangent to the polar curve at the point. r= 2cos(θ/ 3),  θ =π/4

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Q: 5. If z = 2(cos 25° +j sin 25°), find z in polar form.

A: It is simple calculation in polar form

Q: Plot the polar point. (25. 푸) 4 2 3 4 2 4 4. 2. klN 3. 3.

A: To plot the given point

Q: Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form. z = 4√3 -4i,  w = 8i

A: We have to find the polar form for zw, zw and 1z where z=43-4i and w=8i. First, we have to convert z…

Q: (4, − 19π/12)   plot the point with the given polar coordinates

A: The given point is 4,−19π12. The general form of the polar coordinate is r,θ where, r is the…

Q: 2. Find two polar representations for the point having cartesian coordinates (6V3,6). One of your…

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Q: •5 25-x2 Evaluate (x² + y? )° dy dx by converting to polar coordinates.

A: To evaluate the integral using polar coordinates

Q: (4Z30°)² 3. - (6 – 4i)². Express your answer in polar form. - (2cis60°)³

A: Given that: (4∠30°)2(2cis60°)3-(6-4i)2

Q: 1. Transform the polar equation 4 cos 0 cos² 0 + 1 into its Cartesian form and identify the curve.

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Q: Q 2. (a). Express z= 3+ V3i in polar form.

A: Answer (a) We know that if x=x+iy    z=r=x2+y2 ∅=tan-1 yx   x=r cos∅ and y= r sin∅the polar form of…

Q: 2(V3 – i) (1 + 1)?

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Q: 9. 1.7e1.2-/2.5 into polar form Ans.

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

Q: Find zw and W Leave your answers in polar form. - TC TO Z= 6 cos + i sin 11 11 TO W = 6| cos COS + i…

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Q: Convert the given polar equation into an equation in terms of Cartesian coordinates.

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Q: . Show that the equations x = r cos 0, y = r sin 0 transform the polar equation 1 + e cos 0 into the…

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Q: What is (x - 12)² + y² = 144 in polar form? r = 24 sin 0 r= 24 cos 0 O Option 1 r= -24 sin 0-144…

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Q: 2.- Find the value in polar form of the following expressions а) ei1 b) e1-j1

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Q: 3.3. Show that in a polar coordinate system, the distance d between the points (r1,01) and (r2, 02)…

A: The distance between r1,θ1 and  r2,θ2 is d=r12+r22-2r1r2cos θ1-θ2

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

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Q: Write a polar equation of the formr cos(0 – 0) = ro for the line x - V3y = 2.

A: We have to solve given problem:

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…