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Math Help - Straight lines in Argand plane?

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    Super Member fardeen_gen's Avatar
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    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
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    Quote Originally Posted by fardeen_gen View Post
    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.
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