Hello guys, i've done a few more problems that i need corrected, thanks.
1.) The position of a particle in the xy plane at time t (seconds) is given by r(t) = (2 + 5t^2)i + (-3 + t)j
a) find the cartesian equation of the particles trajectory
my answer: x = 5y^2 + 30y +47
b) Sketch the particles trajectory also indicating its direction of motion
my solution: the shape of the graph x = 5y^2 + 30y + 47 is a sideways parabola with a vertex at (2,-3) which was found by completing the square. the particle is travelling in the direction to increase y.
2.) Write the following complex numbers in cartesian form x + iy where x and y are real numbers.
a) (2 - 3i) / (2i - 1)
my solution: -i/8 - 8/3
b) (3-2i)^2 (1+5i)
my solution: 75 + 13i
3.) Find the modulus and argument of z = - (root3)/(10) - 1/10i between -pi and pi.
my solution: arg(z) = - 5pi/6
modulus (z) = 1/5
thanks in advance.