(3+ i) (a) Evaluate 1+i (i) in the form of x+ yi , and polar form r(cos 0+isin 0). 1 (ii) Hence, find the constant values of P and Q if z+== P+iQ by using z in the Cartesian form. SIA
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: 3/2 – 3V2i in Express the complex number z = polar form r cis 0. Select the correct answer below: 5л…
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Q: 3. Find the cartesian equation of r cos 0 = -4 and identify its graph.
A: To find the Cartesian equation of rcosθ=-4 and identify its graph. Solution: In Cartesian…
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A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…
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Q: 3√2 √2 cos 2 2 Consider the polar curves C₁ : r = 4+² cos 0 and C₂ r = 2- as shown in the figure on…
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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: 2. 6 27 4 6 2 Find three additional polar representations of the point, using -2n < 0 < 2n. (Enter…
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Q: 4. Given an equation of a conic in polar formr= f(0), substituting (0 – a) results in a…
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Q: (a). Express z= V3 + V3i in polar form. (b). Find the value of Z if e² =1.
A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…
Q: Graph the line and conic section. r = 8/(1 - sin u)
A: We can convert this into rectangular form. Then,…
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.
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Q: 10. Write –v2 + iv2 in polar form r(cos 8 +i sin 8) where r is exact and 0 so s 2n|
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Q: The polar form Z = 2V3- 2i is Z = 4(cos + isin- 11m O true
A: The given complex form is Z=23-2i
Q: 32 Sketch a graph of r = Use the graph to write a Cartesian equation for the conic. 5 – 3 sin(0)
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Q: 1 a. Showing all 9r2 = (1 + 3r cos 0)². b. Express 9r2 = (1 + 3r cos 0)² in rectangular coordinates.…
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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: (4430°)-(24225°) d. (24140°)(34300°) (Express your answer in polar form)
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Q: 2. a) If -1 o £ 2, give three polar points in the torm of Cr,@) eanivalent to Cartesian point…
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Q: 4 4. a) Identify the conic section given by the polar equation and also determine 1-cos e its…
A: We convert the equation into rectangular form first This is a parabola.
Q: 4. Let z = 4+4i and w = –10i in standard form: (a) Express z and w in polar coordinates, (0 < 0 <…
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Q: 12 Find a Cartesian equation for the polar curver = Solve for y and type the simplified solution in…
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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
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A: Complex number in polar coordinate is given as: z=reiθWhere r=x2+y2 θ=tan-1yx Given complex…
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Q: (2 1 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use…
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Q: √2 2. Consider the polar curves C₁:r = 4 + ³√² cos 0 and C₂: r = 2 - ² cos € as shown in the figure…
A: b. Consider the given polar curves, C1:r=4+322cosθ and C2:r=2-222cosθ the diagram is shown below,…
Q: 20 Sketch a graph of r = Use the graph to write a Cartesian equation for the conic. 3 – 2 cos(0)
A: Given: r=203-2cos(θ) following image represents the graph for the given equation.
Q: 1 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…
A: We need to find coordinates of given point.
Q: a 2 3 4 Identify the coordinates of the point polar form based upon the given conditions. Use pi for…
A: to find the coordinates
Q: 2. a. Sketch the graphs of the rose r = 4 cos20 and the circle r = 2 in one polar plane. Provide a…
A: Given: and Formula used:
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: 6 (1). Consider the curve C of equation (x²-2y+y²)² = x²+y². Among the options listed, select the…
A: We know that a polar coordinate is represented by r, θ, where r is the length with r=x2+y2 and θ is…
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…
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Q: 2. Given z (22 + 0 ) + 4i and = -6 – (8 +0)i. Find w and write it in polar form
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Q: (a). Express z=3 + V3i in polar form. (b). Find the value of z if e- =1.
A: z=3+3i Comparing with z=x+iy, we get x=3, y=3. Now, r=x2+y2=32+32=3+3=6 &…
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: Q4] A complex function in term of polar coordinates, (r,0) is described as f(z)=u(r,0)+j v(r,0). The…
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Q: 3 Find z' in polar form. 4[cos(25°) + i · sin(25°)] 23 cis( %3|
A: Polar form of a complex number
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- find the quotient z1 / z2 in polar form where z1 and z2 are given below. z = 24 [ cos ( 125° )] + i sin ( 125° ) ] and z2 = 4 [ cos ( 37° ) + i sin ( 37° ) ]Given the equation of a conic in the form 8x^2 -12xy +17y^2 -20=0 we can convert this into standard form in the XY coordinate system without the XY term. After finding out what cot(2θ) is, we can use this information to find what sin θ and cos θ is by using the trigonometric identities 2sin^2θ=1-cos2θ and 2cos^2θ=1 +cos 2θ. So, what is the value of sin θ and cos θ?3. Let Z = =11√3i(i) Write Z in a polar form (2)(ii) Use De Moivre’s Theorem to determine Z^4
- 2.11 Let A = p cos 9 ap + pz2 sin az (a) Transform A into rectangular coordinates and calculate its magnitude at point (3, -4 , 0). (b) Transform A into spherical system and calculate its magnitude at point (3, —4, 0).What happened after the second step. What happened to the cos^2vsin^2v.Find all the solution of 6cos^2x+cosx-1=0 on the interval[0,2py]
- In math land, there is a clock. The hour hand of this clock is 1 ft long. However, the clock is weird, in that it takes precisely 2π hours for the hour hand to do a full rotation. Let’s position the clock in the xy-plane so that the center of the clock is at (0, 0), and the tip of the hour hand at "midnight" is at (0, 1). (a) It follows from the definition of sin and cos that at time t, the tip of the hour hand is at position (x, y) = (cos(t),sin(t)). Check that this makes sense by “manually” finding the position of the clock at time t = 0, π/2 , π, 3π/2 , and 2π. (b) The equation describing the circle that the hour hand traces out is x2 +y2 = 1. We’re going to calculate how fast the x-coordinate of the tip of the hour hand changes with time. We’ll do this in two ways. Using the fact that x = cos(t), what is dx/dt ? (c) Next, we’ll compute dx/dt in another way. Using the fact that y = sin(t), what is dy/dt ?In math land, there is a clock. The hour hand of this clock is 1 ft long. However, the clock is weird, in that it takes precisely 2π hours for the hour hand to do a full rotation. Let’s position the clock in the xy-plane so that the center of the clock is at (0, 0), and the tip of the hour hand at "midnight" is at (0, 1). (a) It follows from the definition of sin and cos that at time t, the tip of the hour hand is at position (x, y) = (cos(t),sin(t)). Check that this makes sense by “manually” finding the position of the clock at time t = 0, π/2 , π, 3π/2 , and 2π. (b) The equation describing the circle that the hour hand traces out is x2 +y2 = 1. We’re going to calculate how fast the x-coordinate of the tip of the hour hand changes with time. We’ll do this in two ways. Using the fact that x = cos(t), what is dx/dt ? (c) Next, we’ll compute dx/dt in another way. Using the fact that y = sin(t), what is dy/dt ? (d) Next, use implicit differentiation to find dx/dy . Express your answer…