9.5. If s1 = aj + ib¡ and s2 = a2 + ib2, and s182 = (a¡a2 – bịb2) +i(a¡b2 +azb¡) use the fact that r = Va? +b² and b. -1 = tan a to show that in polar coordinates $1 $2 = (rir2, O1 + 02), S2 O1 – 02 ||

Q: 21) Find the area of a triangle fosmed from the twovectors a = L'+2j-k-.

A: Given, a ⇀=i+2j-kb⇀ =2i-j+4k

Q: Evaluate in polar coordinate 5. So 0 √1-x² (x² + y²)dydx

A: The given integral is ∫01∫01-x2x2+y2dydx. The objective is to calculate the value of the given…

Q: 1. For the polar coordinate (r,0) = (-2,7x/6), give one coordinate rUand -2nsOs 2n.

A:

Q: Find the product Z₁Z2 and the quotient Z₁ = 10(cos(110°) + i sin(110°)), Z1Z2 = Z1 Z2 Z1 Express…

A:

Q: Find the polar coordinate for (-1, √3) where r>0 and 0≤Ø<2π

A:

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

A: Given

Q: Find :L[cos h 5t sin 2t ] 25 2 [(s² – 25)( s² + 4). (s - 5)? +4 O A.) О в) 1 1 1 (s - 5)? +4 (s +…

A:

Q: 5. Find two sets of polar coordinates for the Cartesian point (-7, 7/3) such that 0<0<2T.

A:

Q: Ex. (1): the paralel Sum and difference of the given complex numbers. 1. 2. 3. U = 2+3: U = 4+7i…

A: To add complex numbers in rectangular form, add the real components and add the imaginary…

Q: Q1) Consider two rotations, one about X by 30 degrees and one about Y 60 degrees: Are Rx Ry = Ry Rx…

A:

Q: 2. Convert the polar coordinate (4, 4,=) to Cartesian coordinate

A:

Q: 3. Express 4xi + 5yi° + óxi* + 2yi* in simplest a + bi form.

A: Given z=4xi+5yi8+6xi3+2yi4 To express Z in a + bi Form:

Q: 1. Let 2₁ = 2ej/4 and a) 221-22 b) 12/11 d) 3/2 22 = 8/3. Find

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

Q: 2. Let r>o and Fo tina20 And use polar coordinates KZQ and use polar coordiinates (8,7) >(0,0)

A:

Q: 7. Evaluate JJ S² S² √x² + y²dydx + by converting to polar coordinates. 2√2 1/2v² √²² √2³² + 1²³dyde

A:

Q: Convert 4-j9 to polar form √972-1.1526 Option 1 √972-1.9890 Option 3 √97 21.1526 Option 2 √9721.9890…

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Q: B. Let ul,e)=rMsin(nt). Find Pur tru tUge Orr

A:

Q: Evaluate L{e" cos 41} s+ 4 d) s2 + 8s - 32 4 4 s-4 a) s2 + 8s - 32 b) s2 - 8s + 32 c) s2 - 8s + 32 a…

A:

Q: 38. Which of the following could be polar coordinates for the point with rectangular 1 coordinates…

A: Given co-ordinate: Now,

Q: 2. Convert the rectangle coordinate (1,-√3) to a polar coordinate (r, 0) with r>0,-2л ≤0<2.

A: Given query is to convert rectangular to polar coordinates.

Q: Use De Moivre's Theorem to solve for z and leave your answer in polar form with the angle in radians…

A: If z=rcosθ+isinθ then the nth root is zn=rncosθ+2πkn+isinθ+2πkn and if z=a+ib then r=a2+b2 and…

Q: 6. Convert 5,5/3] to polar coordinates with r positive and between 0 and 27

A:

Q: If A(x₁, y₁), B(x, y₂) and C(x3, 13) are the vertices of triangle ABC and x+y=x2 + y2 = x3 + y3,…

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Q: WWW 45. Convert the polar point (4, 5) to a Cartesian point. A. (-) B. (-) C. (2√3, 2) D. (-2,2√3)…

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Q: 3. Express the following complex numbers in polar form( r< θ), find the modulus ‘r’ and argument θ”…

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Q: 2. a) Given that T, = 2+5f, T, = 4+3i. Find 1. T,+ 27, il. T,- 47, T iv. 10(T, – T,) b) Express T,…

A: See the attachment

Q: Show that sin , +sin ¤, = 2 cos[;(4, – Þ,)]sin[;(P, +Ð,)]

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Q: 3. Evaluate LLA" (4- y2) dydx by using polar coordinates.

A:

Q: Determine the period of the sinusoidal function y=-3 sin| 2| x- -~-3 m 2 ( x − 3 ) | + -- +1. a) 1…

A: If y = A*Sin(B(x+C))+D is the sinusoidal function, then Amplitude = A Period = 2π/B Phase Shift = C…