6) Let f(z)=(2²-z-1)7. If a²+a+1=0 and Im(a)>0, then find f(a). a) 128a b) -128g c) 128g² d) -128g² 7) c(z+1)+dz= where c is the circle |z)=3 a) 4e b) 4 c) 4¹ d) 8ni 3

Q: Which function has a y-intercept of -2? O 3x + 2 a) fx) = 5х -1 3x + 2 O b) Ax)· 5x- 1 Oc) Ar) = 5x…

A:

Q: Q2 a) { ] Show that the equation 4x - 8y + 12z + 2x² + 2y² + 2z² = −20 represents a sphere, and find…

A:

Q: 30) The coordinates of the endpoints of line segment CD are C(–4, 1) and D(3, 4). Reflect the line…

A: x-axis is also known as the principal axis . The y-coordinate of the point that lies on x-axis is 0.

Q: i æ² + y? = 30 and (x + 1)? + (y – 1)² = 6 | ii (æ + 3)? + (y – 2)² = 9 and (x + 7)? + (y + 1)? = 4…

A: (i) The given circle is: x2+y2=30        ....1x+12+y-12=6       ....2

Q: ) Calculate (8(x² - y)i + 8(y² + x)j³) · dř if: (a) C is the circle (x − 4)² + (y − 8)² = 25…

A: (a) We have to calculate  where .in parametric form Now  and Now

Q: (0,1,1) to the line of intersection of the planes : x + 2y + z = 1 x - y + 2z = -8

A:

Q: the line a1x+b1y+c1=0 and a2x+b2y+c2=0 cut the coordinate axes at concyclic points,then prove that…

A:

Q: In the projective plane, Z5P2, find the line that contains the points (1,2,1) and (2,1,4).

A: In projective geometry over a finite field, such as , we can find the line that contains two points…

Q: 22.) Determine if the graph of the relations below are symmetric w/ respect to a) the x-axis, b.)…

A: Given:The functions are:a) b) c) Aim:To check whether the functions are symmetric abouta) the…

Q: Show that 25+ 2z² + 3z + 2 has five zeroes inside the circle |z| = 2, and determine the number of…

A: If f(z) and g(z) are two analytic functions within and on a simple closed curve C such that |f(z)|…

Q: Find the tangent hyperplane (i.e. linear approximation) to the hypersurface in R4: h = 1 = xy + x²z…

A:

Q: a) [ ] Show that the equation 4x8y + 12z + 2x² + 2y² + 2z² = -20 represents a sphere, and find its…

A:

Q: Q6. Let O(0,0), A(1,0), B(1,4) be points in the plane R². Then the following point lies in the…

A: I am attaching image so that you understand each and every step.

Q: 3. Sketch the parallelogram spanned by (2, 1, 0) and (-3, 1, 0) in the xy plane and find its area.

A:

Q: Which point(s) lie in the plane 2x + y - z = 10? a) (0, 0, 10) c) (2, 4, - 2) b) (5, 3, - 3) d) (-3,…

A: Given:plane: 2x+y-z=10

Q: Q)Suppose that one line is parallel y=13x+ 13 and passes through (15,7). Where does that line cross…

A: Given :  y=13x+ 13  compare with y = mx + c slope m = 13

Q: Let C be the upper half (yzo) of the circle x² + y2 = 16 from (4,0) to (-40). √ (ax 2-3y) ds =

A:

Q: write the quation of the perpendicular bisector that gose through the lie segment with end points of…

A: The perpendicular bisects will be passing through the midpoints of the given points A(4,-1) and…

Q: △ABC△ABC has vertices A(0,4), B(6,-1), and C(3,7). What are the coordinates of C' when the triangle…

A:

Q: The shortest distance from (−7,6,−8) to the xy-plane is

A: Since the plane is a xy-plane so, the point will be (-7,6,0).

Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: Use equation of plane

Q: Please

A:

Q: 11) Determine the equation of the line parallel to y - 57 = -4(x + 58) that contains the point (95,…

A: Question number 11,Given,        The equation of the line parallel to y-57=-4x+58 that contains the…

Q: Consider the autonomous DE x' = x(x – 1)(x + 2). Determine the critical points of the equation.…

A:

Q: Calculate 5z $c C (z2-z-2) (z²+i8z-16) where C is the circle a) |z|=1 b) |z|=3 c) |z|=4 dz

A:

Q: Let f(x)= 56-2) (x+1 What is the domain? b find all x-intercepts OFind y-intercept if it exists?

A:

Q: Prove that the length of common chord of the two circles x + y² + 22x + c = (2² -c)(µ² +c) 2² + µ? O…

A: We will prove that the length of the common chord is the given term as following.

Q: Fud the Line pussing through the posnt (!,-l,o) and purrllel to the Eme of intersection of planes (X…

A:

Q: When the ratio test is applied on the power series > Cn(x – 4)", the resulting limit is Which of n=0…

A: Here we use ratio test formulas.

Q: Sketch the graph of the following quadratic surfaces a) 4x² +9y² + z² = 36 b) x²y² 2²=1 c) x² +…

A: Given the equation of curves.

Q: d) z = −2x² - 4y² e) x = z² - y² f) y = √x² + 3z²

A:

Q: 2. Sketch the line = : (−2,−3) + t(3,4), and label 3

A: An equation of the formhas x-intercept a and y-intercept b.