1.     Create a Complex Number Parameter Equation (use the Parameter Equation formula (z(t)=x(t) + y(t)i ). Straight Line from 1+ i to 4-2i

Q: This is question of Complex Analysis.

A: I am providing the solution of (ii) only as follows below :

Q: a) Find the parametric equation of the line that passes through points S (2,-1,3) and T (-1,1,-2).…

A: We have to do the complex number problem and equation of line

Q: Q2) Verify v(x.y)-3x3y-y3+5x is harmonic in the entire complex plane then find the conjucte harmonic…

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Q: Let f (2) = z2 + 12 + 18ė a complex function. What is the image of the line x = 2 A straight line A…

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Q: 4) Find the critical points of the parametric equations x = t* - 1 y = t3 - t

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Q: The following are parametric equations of the line through (x1, y1) and (x2, y2): x = x1 + t(x2 -…

A: From x = x1 + t(x2 - x1) we get: x-x1=tx2-x1 t=x-x1x2-x1   From y = y1 + t(y2 - y1) we get:…

Q: Find the parametric equations for the ellipse y2 + 4x2 - 2y + 4x + 1 = 0. Hint: Use completing the…

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Q: evaluate ∫c (x-iy) +Im(2z) dz where C is a curve starting at −2, follows a vertical line to reach…

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Q: Find a parametric equation of the line tangent to 7 (t) at the point (– 12, 144, – 4.159)

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Q: 2. Find the parametric equations of the line passing through the point (-1,4, –3) and is parallel to…

A: Given information is as below: r0=(-1,4-3)v=5i-j=(5,-1,0)

Q: Ecample 12: Show that the equation of a straight line in the Argand plane can be put in e form zh +…

A: GIven the equation of straight line

Q: Describe the graph of the equation. r = 10 cos ti + 3 sin t j – k O Itis an ellipse in the z = -1…

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Q: 1. a) Find parametric equations of the line of intersection of the planes 3x- 2y+z=0 and…

A: Given : equation of a plane, 3x-2y+z=08x+2y+z-11=0

Q: Let f (z) = z² + 3+11i be a complex function. What is the image of the line x = 10 A straight line A…

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Q: 4

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Q: Q6) The parametric equation of the x_axis is: * O t-1 O x=0 O x=t O x=1

A: Since at x-axis, y and z axis are both zero and only x is varying so general parametric equation for…

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: Wrte cach equation In expotentiai form. 16) logs=-3

A: 16. Given: log3127=-3 Identity of exponents: logab=c can be expressed as ac=b.

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

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Q: Find the parametric equation of the line that passes through P(1, 0, -3) and is parallel to the line…

A: Given: We have to find the parametric equation of the line that passes through the point P(1, 0, -3)…

Q: evaluate ∫c +Im(2z) dz where C is a curve starting at −2, follows a vertical line to reach −2+i and…

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Q: d. P = 4x1 – 2x2, Q = 2x1 + 6x2; D is the interior of the ellipse: x1 = 2 cos 0, x2 = = sin 0, 0 E…

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Q: ») Shade the region in the complex plane defined by {rec: s |z+ 2+ 2i <1 4i E C

A: Complex plane

Q: e a Co

A: Introduction: A parametric equation is one in which the dependent variables are defined as…

Q: The following are parametric equations of the line through (x1, y1) and (x2, y2):x = x1 + t(x2 - x1)…

A: Given: the parametric equations of the line through (x1, y1) and (x2, y2)x=x1+t…

Q: Eliminate the parameter in the parametric equations a(t) = log (12t) and y(t) =-3t + 2 to a…

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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: 5. Find the parametric equations of a line through (1, 0, -1) and parallel to the line -(x-4) 1 y =…

A: Consider the given equation of the line. Converting it into the standard form and taking the…

Q: 1.4 Describe and sketch the curve in the complex plane given by 21리 3 1z- 21. Also write your final…

A: We have to Describe and Sketch the curves in the complex plane given by 2|z|=|z-2| Also write final…

Q: If a, b are complex constants and a real parameter, what does the equation z = a cost+bsint…

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Q: Pls help ASAP

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Q: Find all integer solutions to the linear Diophantine equation, 0.05x + 0.14y +0.35= 10.29. Write…

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Q: 1.4 Describe and sketch the curve in the complex plane given by 2|2| = |2 – 2|. Also write your…

A: We assume z=x+iy then we put this value on the given equation to find the curve and from curve we…

Q: 1. 1. Define: u(x,y) is harmonic. Explain how this is relevant to complex variables.

A: Define u(x,y) is harmonic , complex variables

Q: *+ xx + x = 0 has a centre at the origin. %3D

A: Given: x.. +xx.+x3=0

Q: Find the parametric equations of the line segment through the origin and perpendicular to the plane…

A: Given: Given equation of the plane is x-2y+3z=5 We want to find the parametric equations of the line…

Q: Find y as a function of t if 7y" + 28y = 0, y(0) = 4, y'(0) = 3. y(t) Note: This particular weBWork…

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Q: x+4 5 y-2 -5 2+1 1

A: Given the equation is x+45=y-2-5=z+11

Q: (c) Find parametric equations to represent the red line in the graph below. 10 (-2, 7) (6, 3) -5 10…

A: This is a problem related to equation of line. Based on the general formula of line equation we will…

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

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Q: 6) Find parametric equations for the line through P(0, -2,-2) and Q(1,1,0).

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Q: Find y as a function of t if 3y" + 31y = 0, y(0) = 7, y'(0) = 3. y(t) Note: This particular weBWork…

A: A differential equation with initial conditions is called the initial value problem. The solution of…

Q: A hiker in the woods travels along the path described by the parametric equations X = 80 − 0.7T Y=…

A: Hiker  X=80-0.7T Y=0.3T   Bear  X=0.2T Y=20+0.7T

Q: Find the cartesian equation of the curve

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Q: 5. Find the angle or rotation and new equation of curve 5x2 - 6xy +5y2 - 12 = 0 such that the…

A: Consider the general equation Ax2+Bxy+Cy2+Dx+Ey+F=0is rewritten asA'x'2+C'y'2+D'x'+E'y'+F'=0by angle…

Q: Find a parametric representation of the solution set of the linear equation. (Enter your answer as a…

A: Introduction: A parametric equation is one in which the dependent variables are defined as…

Q: find parametric equations for the given curve. 4x − y2 = 5

A: Given curve is:

Q: (b) Find the graph of the parametric equations: I = sin 0, y = 3 – 2 cos 20

A: Plugging values of θ, to find the corresponding values of x and y: When…

Q: Let f (z) = z² + 9+ 10i be a complex function. What is the image of the line x = ? A straight line A…

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Q: 2. (a) A curve has parametric equations x= 3 - 2cos 0and y = sin 8. Determine the Cartesian equation…

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