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

Originally Posted by fardeen_gen

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

Write z= x+ iy so that $\displaystyle \bar{z}= x- iy$. 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.