- #1

Bacat

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*This is not homework, though a class was the origin of my curiosity.

In real analysis we could find the equation of a line that passes through two points by finding the slope and then plugging in one set of points to calculate the value of b. ie

[tex]y = mx + b[/tex]

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

In complex analysis, we know that the equation for a line is [tex]Re[((m+i)z+b)]=0[/tex]. Sitting down to derive m, I find the following:

[tex]m = \frac{Im[z_1] - Im[z_2]}{Re[z_1]-Re[z_2]}[/tex]

But if I try to plug in the points (say [tex]z_{1}[/tex] and [tex]z_{2}[/tex]), it doesn't give me a value for b that makes sense. what is the correct way to find the equation of a line?

In real analysis we could find the equation of a line that passes through two points by finding the slope and then plugging in one set of points to calculate the value of b. ie

[tex]y = mx + b[/tex]

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

In complex analysis, we know that the equation for a line is [tex]Re[((m+i)z+b)]=0[/tex]. Sitting down to derive m, I find the following:

[tex]m = \frac{Im[z_1] - Im[z_2]}{Re[z_1]-Re[z_2]}[/tex]

But if I try to plug in the points (say [tex]z_{1}[/tex] and [tex]z_{2}[/tex]), it doesn't give me a value for b that makes sense. what is the correct way to find the equation of a line?

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