Solve the following: 1. (x-2iy)-(y-ix)=2+i, x=?; y=? Express in Polar Form: 1. 3+i4 2. -3+i4

Q: 4- The equivalent of Cartesian equation (x + = 1) in polar equationis:

A: Given: Cartesian equation:   To determine: equivalent polar equation.

Q: 7. Solve the eight eighth roots (in polar form) of z = -2- j2/3. %3D

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Q: roo (b) Еxpress e-(2²+y²) dyd.r in terms of d.r, and hence compute e dr.

A: In this question, we express the integral as ∫-∞∞∫-∞∞e-x2-y2dydx  in term of ∫-∞∞e-x2dxand then…

Q: Convert the Cartesian equation to a polar equation that expresses r in terms of 0. x + (y + 5)? = 25…

A: The equation in rectangular coordinates is given by x2+y+52 = 25 To evaluate : The polar equation…

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

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Q: B- If (Z₁ = (3+ i5) and Z₁ = (2- i3) By using Polar form to find Z₁x7₂ 21.01722.721° 23.01722.721°…

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

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

A: Given

Q: Convert to polar form. Then isolate r. (a) x² +y² -9= 0 (b) x² +y = 4x %3D

A: x2+y2-9=0 On simplification, we get ⇒x2+y2=9⇒r2=9         ∵r=x2+y2⇒r2=x2+y2⇒r=3

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: Express the following complex number in its polar form.

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Q: Find the product z₁z2 and the quotient Express your answers in polar form. 2₁ = 2(cos() + / sin()),…

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

A: Solution-

Q: Simplify (-V3+ i)*. 8e2i 5e-0.7i Determine the quotient of in polar form. O-8 – 12. 856 i 1. 6838e…

A: (1) -3 + i4 = (-32 + i2 - 23i )2                   = 2 - 23i2                  = 4 - 12 - 83i…

Q: Convert the polar point (1,57/3) to an equivalent polar point where r < 0 and 0 <0 < 2T. O A. (1,…

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Q: in C6. Evoluate the Rxpiession, write your ans wer polar and rectangulor form

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Q: Q5/ Change the polar equation 2r = 2 + cos 0.(2r-1) to Cartesian equation Ans./y²-3x² - 4x-1=0

A: To find- Change the polar equation 2r = 2 + cosθ·2r - 1 to Cartesian equation.

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

A: Given co-ordinate: Now,

Q: Dmitry and Sofie were converting the rectangular equation, x² - y² = 5y + 3 to polar form. They each…

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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: 1.3 + j4 2. –3 + j4 3. –3 – j4 4. 3 - j4

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Q: +If z = 4el3, determine In z (a) in Cartesian form, and (b) in polar form Į Determine in polar form…

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

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