4. Let z = 1+ V3i. (a) Graph z in the complex plane. (b) Write z in polar form. (c) Find the complex number 2°.

Q: 14 Sketch a graph of r Use the graph to write a Cartesian equation for the conic. %3D 3 – 4 cos(8)

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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: Sketch a graph of the polar equation. C-8 sin(e) /2 /2 10 10 -10 -5 10 -5 -5 -10- /2 /2 10 -10 10…

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Q: 36 Sketch a graph of r = Use the graph to write a Cartesian equation for the conic. 4 + 5 sin(0)

A: Sketch the graph of r=364+5sinθ as shown below.

Q: Sketch a graph of the polar equation  r = −3 cos 2θ

A: We will make a table for the function.

Q: Sketch the graph of the polar equation.r = 4(1 - θ)

A: To sketch the graph of the polar equation, r=4(1-θ), first, find the values of r corresponding to…

Q: 4. Write down the name of the conic given by the polar curve r = 15 / (3 + 2 sine). Determine the…

A: We have to draw graph of given curve.

Q: I. Write 2 – 7i in polar coordinates on the complex plane. II. Find (1+ i)° using DeMoivre's…

A: z=2-7ia=2, b=-7z=a2+b2     =4+49|z|=53θ=tan-1baθ=tan-1-72θ=-tan-172Polar form:=z cos-tan-172+…

Q: Vz + i/3 V3 - 10i 5. 6. -V8 – 21/3 -V3 + 5i

A: The given problem is to evaluate and simplify the given complex expression and graph the following…

Q: Sketch a graph of the polar equation  r2 = 9 cos 2θ

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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: Test r2 = 9sin 2θ for symmetry and then graph the polar equation.

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Q: 14 Sketch a graph of r = Use the graph to write a Cartesian equation for the conic. 4 + 3 sin(0)

A: To Sketch: i. r=144+3sinθii. Use a graph to write the cartesian equation for the conic. Explanation:…

Q: 18 Sketch a graph of r = Use the graph to write a Cartesian equation for the 5+ 4 cos(0) conic.

A: Given equation, r=185+4 cosθ                                  ...(1)

Q: Identify and draw the conic r(2 – 2 sin 0 ) = 8. %3D

A: We have to solve given problem:

Q: Sketch the graph of the polar equation.r = 3 sin 2θ

A: Solution:Given     r= 3 sin2θTo sketch the graph of the polar equation.

Q: Identify the conic section and graph the polar equation: r = 2/(1 - cos θ)

A: The given polar equation is r=21-cosθ Here, the given equation can be ellipse, parabola and…

Q: (b) If z = x + iy is a complex number. Sketch the curves in the complex plane given by i. Im(2) = –1…

A: i. Given that Imz=-1. This implies that, Imz=-1Imx+iy=-1y=-1 Sketch the curve Imz=-1 as shown below.

Q: 29. When z = z If z and z are equal, what can you say about the location of the point z in the…

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Q: Find the set of points satisfying the equation in the complex variable z: |z* + 2i| = I(z − 3i)|…

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Q: 3 Identify the conic represented by the polar equation r 1 Find the rectangular equation. 2 cos 0

A: Given equation, r=31-2cosθ                              ....(1)

Q: 4. Write down the name of the conic given by the polar curve r = 15/( 2 sine). Determine the…

A: Given the polar curve is r=153+2sinθ

Q: 3. Find the polar form of the Cartesian equation: x² + y² = (3 + 2x)² %3D

A: Solution-

Q: 2. Find the set of points satisfying the equation in the complex variable z: |2* + 2i| = |3(z – 3i)|…

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Q: Find the areas of the regions in the polar coordinate plane described Enclosed by one leaf of the…

A: Area of the region bounded by r=fθ between the radial line α to β is A=12∫αβr2dθ

Q: Q1 Rewrite the polar equation r= 2sinecose in Cartesian form-

A:

Q: 1. Describe and sketch the curve in the complex plane given by 2|z| = |z-2| Also write your final…

A: We have to Describe and sketch the curve in the complex plane given by2|z| = |z-2|Also write your…

Q: Sketch the graph of the polar equation.r2 = 4 cos 2θ (lemniscate)

A: The polar equation is,r2=4 cos 2θ

Q: 9. (a) Find the rectangular coordinates of the point(s) of the graph of the polar equation r = 4 sin…

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Q: Sketch the graph of the polar equation.r = 2 sin 4θ

A: Given: r = 2 sin 4θ

Q: Sketch a graph of the polar equation  r = 4 − 3 cos θ

A: Given polar equation:                                     r = 4 − 3 cos θ

Q: Question 7 Describe and plot the points z in a complex plane defined by the following region: A = {:…

A: z is a complex number. A=z∈ℂ:Reiz¯2<3∩z∈ℂ:z+2i<4

Q: Identify and draw the conic r(2 + sin 0 ) = 6.

A: In this question, we have to identify the conic and draw it.

Q: 28 Sketch a graph of r = Use the graph to write a Cartesian equation for the conic. 4+ 3 sin(0)

A:

Q: 8. the same graph as the polar equation r-6cos0 =0 and graph on the xy plane. Find an equation in x…

A: The given polar equation is r-6cosθ=0 The equation in x and y is to be calculated and graphed in the…

Q: Find the set of points satisfying the equation in the complex variable z: |z* + 2i| = |F(z – 3i)|…

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Q: 3. Write down the name of the conic given by the polar curve r = 6/ (2 - sine). Determine the…

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Q: 22 Sketch a graph of r = Use the graph to write a Cartesian equation for the conic. 6 + 5 sin(0)

A: Given  r=226+5sinθ For a conic with focus at origin , directrix  y=±p, p is a positive real number…

Q: Sketch a graph of the polar equation. r = 1- 2 cos 0 A/2 A/2 3 2 1 -2 1 3 -3 -2 -1 3 -2 -3 л/2 A/2 3…

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Q: Sketch the graph of the polar equation.r = -6(1 + cos θ)

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Q: 44 Sketch a graph of r = Use the graph to write a Cartesian equation for the 6 + 5 cos(8) conic.

A: Sketch the graph of the conic  r=446+5cos θ using a graphing calculator as shown below.

Q: 2.1 Given the complex number z=3-j. 2.1.1 Show z on an Argand diagram. 2.1.2 Rewrite z in polar…

A: As per guidelines we are supposed to solve the maximum first question at a time. kindly post another…

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

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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: Find the values of z such that z^5 = −i. Write your answers in polar form and sketch their location…

A: The given complex equation is z5=-i. To find: All the roots of the complex equation.   Using the…

Q: Graph the polar equation r= 1 - 2 cos 0. %3D

A: