- #1
loonychune
- 92
- 0
Just want a check of this please:
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 :)
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 :)