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

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The discussion focuses on sketching the complex curve defined by Z(t) = t^2 - 1 + i(t + 4) for the interval 1 < t < 3. Participants clarify that the x-axis represents the real part (x = t^2 - 1) and the y-axis represents the imaginary part (y = t + 4). The transformation of the y-equation allows for substitution into the x-equation, resulting in a parabolic equation x = (y - 4)^2 - 1. The graph is confirmed to be a parabola with a horizontal axis, and participants inquire about the vertex of this curve. The conversation concludes with a confirmation that the graphing approach is correct.
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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
 
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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?
 
Yeap i can graph that ... is the curve that i need right ?
 

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