please solve Let z1 = 5-i and z2 = -5+3i be complex numbers. Find z1 - z2 z1z2 z

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Let z1 = 5-i and z2 = -5+3i be complex numbers. Find z1 - z2 z1z2 z1/(2z1+z2) Express the exact value of all answers in standard form. Let z = z1+z2. Find the magnitude of z and the principal argument of z and use these values to find exact values for the square roots of z. Let l1 be the line having parametric equations x=1+3s, y=2-s, z=-1+2s and l2 be the line having parametric equations x=8+t, y=-5+2t, z=7-t. By finding the point of intersection, show that l1 and l2 intersect. Find the cosine of the angle between the lines at the point of intersection. Let f(x, y) = 6 . Find the first partial derivatives of f. Find the equation of the tangent plane to the surface defined by f at the point (2, 1) in the domain of f. Use a linear approximation to estimate the value of f(-2.94, 3.04). The following results may be helpful:

Explanation / Answer

4)

1+3s = 8+t

2-s = -5+2t

-1+2s =7-t

s =3, t=2 satisf all so they intersect.

cos theta = (3-2-2)/sqrt(14*6) this will give you theta.

5) fx = 6x/sqrt(x^2+y+4)

fy = 3/sqrt(x^2+y+4)

fx(2,1) = 6*2/sqrt(4+1+4) = 4

fy(2,1) = 1

f(2,1) = 6*sqrt(4+1+4) = 18

so tangent 4x + y = c

Now tangent should satisfy (2,1)

4*2 + 1 = 9

so tangent equation 4x + y = 9

Now to find f(-2.94,3.04) we first find value at nearest point (-3,3)

f(-3,3) = 6*sqrt(9+3+4) = 24

fx(-3,3) = -18/4 = -9/2

fy(-3,3) = 3/4

so f(-2.94,3.04) = 24 -(9*0.06/2) + (3*0.04/4) = 23.7

This answer is correct plz rate it

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