Sketch Curves Z(t)= t^2 - 1 + i(t+4) 1<t<3

[nesett]

Z(t)= t^2 - 1 + i(t+4) for 1<t<3

Can anyone Sketch it for me I m new on the forum ... and don't know how to skecth it

 

[HallsofIvy]

I take it that is in the complex plane. Taking the x-axis to be the real line and the y-axis to be the imaginary line, x= t^2- 1 and y= t+ 4. From y= t+ 4, t= y- 4. Replacing t in the x equation with that, x= (y-4)^2- 1. That's a parabola with horizontal axis. Can you graph that? Where is the vertex?

 

[nesett]

Yeap i can graph that ... is the curve that i need right ?