Complex plane mapping
Show that the mapping w = z +c/z, where z = x+iy, w = u+iv and c is a real number, maps the circle |z| = 1 in the z-plane into an ellipse in the (u, v) plane.
Did you find an error or inaccuracy? Feel free to write us. Thank you!
Thank you for submitting an example text correction or rephasing. We will review the example in a short time and work on the publish it.
Tips for related online calculators
Try our complex numbers calculator.
You need to know the following knowledge to solve this word math problem:
We encourage you to watch this tutorial video on this math problem: video1
Related math problems and questions:
- Intersection 19343
What is the sum of all coordinates of points at the intersection of the line p: x = -1-2t, y = 5-4t, z = -3 + 6t, where t is a real number, with the coordinate planes xy and yz?
- Find the 15
Find the tangent line of the ellipse 9 x² + 16 y² = 144 that has the slope k = -1
- ABS, ARG, CONJ, RECIPROCAL
Let z=-√2-√2i where i2 = -1. Find |z|, arg(z), z* (where * indicates the complex conjugate) and (1/z). Where appropriate, write your answers in the form a + i b, where both a and b are real numbers. Indicate the positions of z, z* and (1/z) on an Argand d
- Complex number coordinates
Which coordinates show the location of -2+3i
- Roots count
Substitute the numbers/0,1,2,3/into the equation as x: (x - 1) (x - 3) (x + 1) = 0 Which of them is its solution? Is there another number that solves this equation?
Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: (x-x_S)2+(y-y_S)2=r2
- Parallel and orthogonal
I need math help in this problem: a=(-5, 5 3) b=(-2,-4,-5) (they are vectors) Decompose the vector b into b=v+w where v is parallel to a and w is orthogonal to a, find v and w
- Fractions and mixed numerals
(a) Convert the following mixed numbers to improper fractions. i. 3 5/8 ii. 7 7/6 (b) Convert the following improper fraction to a mixed number. i. 13/4 ii. 78/5 (c) Simplify these fractions to their lowest terms. i. 36/42 ii. 27/45 2. evaluate the follow
- Find parameters
Find parameters of the circle in the plane - coordinates of center and radius: x²+(y-3)²=14
- Function x*tanx
Functions: f(x)=xtanx f(x)=(e^x)/((e^x)+1) Find; i)vertical and horizontal assyptotes iii)the interval of decrease and increase iii)Local maxima and local minima iv)interval of concavity and inflection. And sketch the graph.
- Find radius
Find the radius of the circle using the Pythagorean theorem where a=9, b=r, c= 6+r
From the equation of a circle: 2x² +2y² +20x -20y +68 = 0 Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.
- Find the 13
Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3], and C[9, 4].
- Francesca 2
Francesca applied the steps below to find the product of (-1.2)(-9.4). Step 1: (-1.2)(-9.4) = (-9.4)(-1.2) Step 2: = (-9.4)(-1) + (-9.4)(-0.2) Step 3: = (9.4) + (1.88) Step 4: = 11.28 Which step shows
- Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
- Intersection of Q2 with line
The equation of a curve C is y=2x² - 8x +9, and the equation of a line L is x + y=3. (1) Find the x-coordinates of the points of intersection of L and C. (ii) show that one of these points is also the
Find the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: 5x ² +9x + q = 0