Parametrization in Complex Integration

[ColdFusion85]

I have a complex analysis final exam on Wednesday, and I am studying the section on complex integration. I am having trouble seeing how to parametrize an equation.

"\Gamma is the line segment from -4 to i"

In the homework solutions our TA said, "Parametrize \Gamma by z = -4 +t(i+4), 0<t<1"

I know this is probably simple algebra stuff, but how would I determine this?

 

[cristo]

The general parametric equation for a line from a point x to a point y is x+t(y-x). This is just standard geometry.