(a) If z = -1+i then determine | z| = r and Arg( z) = 0 and write z in polar form: z = r(cos 0 + i sin 0). (b) Apply De Moivre's Theorem to express z® = (-1 + i )³ in the form a + b i . (c) Find all cube roots of z = -1+i in polar form and then plot them in the complex plane.

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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: 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: Test for symmetry with respect to the line 0 = T/2, the polar axis, and the pole. (Select all that…

A: To solve the following problem

Q: B/Test the symmetric of polar equations: 1- r= 1+5 cos 0 2- r= 3 sin 0

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Q: 4 1-2 sin 0 equation of the conic (b) Given r=- Find the distances from the pole to the vertices and…

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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: Z= [* / (2- 1/1 ) + i] Express Z in polar form; in exponential form; in trigonometric form

A: Explanation of the answer is as follows

Q: 29-46 Sketch the curve with the given polar equation by first sketching the graph of r as a function…

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Q: a) Given u = 2 – i and v = i – 3. Express in the form a + ib. u? + v Hence, determine the modulus…

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Q: III-1. If z = 5e3 2, find In z in polar form correct to three decimal places. a) 3.582263.306° b)…

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Q: Test for symmetry with respect to the line 0 = t/2, the polar axis, and the pole. (Select all that…

A: It can be find by putting the required condition of curve and the angle.

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Q: 120 (a) Find the constants a,b,c for the conic r= Sketch the conic. 5+sin 0 4 (b) Given r = . Find…

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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: The polar equation of a conic section, whose eccentricity e = 5 and the directrix x = 7 is 35 r= 1-5…

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Q: 6. Consider the polar equation r = 2 – 2 cos(0) a) Complete the table of values for r = 2 -2 cos(0).…

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Q: 1. Sketch the graph of point P with the (2.) a. 4 2. Find the polar coordinates that correspond to…

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

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Q: b) Consider the polar equation r = 3 sin(30). i. Test the symmetries for the above polar equation.…

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Q: (a). Express z = V3 + V3i in polar form. (b). Find the value of z if e =1.

A: (a) Consider the given function as z=3+3i It is the equation of complex number in the form of a+ib

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

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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).…

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Q: = -V2 – V2i in Express the complex number z = – polar form r(cos 0 + i sin 0). Select the correct…

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Q: Describe the graph of the equation. r = 7 cos ti - 9 sin t j + k major axis of length 7 parallel to…

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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 &amp;…

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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: 1. Use de Moivre's theorem to find all solution to 25 +32i = 0. Give the solutions in polar form…

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Q: 2-j in polar form. Express the principal root in 1+ j2 Q3/ Find the three cube roots of Cartesian…

A: Topic-Complex