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We have a complex equation of the form az+bz*+c=0

where a, b and z are complex #s, c is real...

If you take the real and imaginary parts of such an equation you obtain two linear equations in x and y, whose solutions of each gives rise to a line (L_1 and L_2 respectively)....

The set then, of solutions, is L_1 unison L_2

Now, the set of solutions of the complex equation is either empty, a point, or a line....................the book gives these 3 examples as each case:

z + z* = i

z+2z* = 0

z+z* = 0

I don't understand how z+z*=0 is a line... for we in fact have

RE(Z+Z*)=2x=0

IM(Z+Z*)= 0y = 0

which then gives rise to a point solution does it not??

if it was z+z* = c say, then i could see that having a line of solutions but as it is, i reckon the book has made an error..... is this the case???

(perhaps i have confused the issue and if that is the case maybe then you coudl point out how my thinking is wrong)

THANKYOU :)

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# Equation of a Line

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