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Homework Help
Precalculus Mathematics Homework Help
A straight line in the complex plane
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[QUOTE="rajeshmarndi, post: 6160018, member: 179607"] [B]Homework Statement:[/B] w+w* = (s+t*)z + (t+s*)z* + r+r* = 0, is a straight line. Then couldn't find how does w-w* = (s-t*)z + (t-s*)z* + r-r* = 0, is also a straight line. [B]Relevant Equations:[/B] w = sz+tz*+r=0 sz+tz*+r=0=say w so w* = s*z* + t*z + r*=0 Now , w+w* = (s+t*)z + (t+s*)z* + r+r* = 0 = p*z + pz* + k = 0...eq(1) ( k is a constant or twice real part of w) which is in complex straight line equation form i.e ab* + a*b + c = 0 ( a,b are complex number and c a real number. Now, again, w-w* = (s-t*)z + (t-s*)z* + r-r* = 0 I couldn't understand, in the solution, how this is also termed as a complex straight line like eq(1). Since when this is worked out, it comes to be as, q*z - qz* + id = 0 ( since r-r* will give imaginary number) This is not in the form of a complex straight line equation. Thanks. [/QUOTE]
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Precalculus Mathematics Homework Help
A straight line in the complex plane
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