Author Topic: Problems to 1.2 Q20  (Read 330 times)

Jessica Long

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Problems to 1.2 Q20
« on: September 22, 2020, 10:44:50 PM »
The question: Let z1 and z2 be distinct complex numbers. Show that the locus of points z={tz1+(1−t)z2,−∞<t<∞}, describes the line through z1 and z2. The values $01 give the line segment joining z1 and z2.

I have an intuitive understanding of why the locus is a line, as it is similar to the description of a line through two points in R^2. However, I'm not sure how to prove this holds in C. Should I be trying to express it as one of the equations for line in C, such as Re(n̄z) = C or w̄z + wz̄ = r?

Victor Ivrii

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Re: Problems to 1.2 Q20
« Reply #1 on: September 23, 2020, 07:58:36 AM »
You ca refer to the fact that straight lines in $\mathbb{C}$ are also straight lines in $\mathbb{R}^2$ and conversely