# Straight lines in Argand plane?

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• Apr 30th 2009, 07:06 AM
fardeen_gen
Straight lines in Argand plane?
In an Argand Plane, the equation $(m + i)z + (m - i)\bar{z} + 2c = 0$ represents slope intercept form of straight line where $m$ is the slope and $c$ is the imaginary axis intercept. Prove it. Also show that if $a$ and $b$ are intercepts of a straight line on real and imaginary axes respectively, then its equation is $(b - ai)z + (b + ai)\bar{z} = 2ab$
• Apr 30th 2009, 08:32 AM
HallsofIvy
Quote:

Originally Posted by fardeen_gen
In an Argand Plane, the equation $(m + i)z + (m - i)\bar{z} + 2c = 0$ represents slope intercept form of straight line where $m$ is the slope and $c$ is the imaginary axis intercept. Prove it. Also show that if $a$ and $b$ are intercepts of a straight line on real and imaginary axes respectively, then its equation is $(b - ai)z + (b + ai)\bar{z} = 2ab$

Write z= x+ iy so that $\bar{z}= x- iy$. Your equation become (m+ i)(x+ iy)+ (m- i)(x- iy)+ 2c= 0. Multiply that out and show that it can be written as the equation of a line in x and y.