Your simplification is wrong
Now equating real and imaginary parts gives
and .
So the solutions are and .
Hey guys, quick question
(b) Find all complex solutions of iz + z = 0 and sketch them in the complex plane.
Well I let z = x + iy, simplified and obtained x - y + i(x - y) = 0
But as for sketching them I'm not entirely sure how to proceed. The answers have up and until the answer I obtained but then immediately proceeds to sketching y = x
Can someone please explain why y = x is the solution?
The equations and have to be true simultaneously. Therefore the only solution is x = y = 0.
But the OP has not actually typed the correct question. The correct question is probably the following:
Find all complex solutions of and sketch them in the complex plane.
In which case, you end up with the two equations x - y = 0 and x - y = 0 and the solution is obviously y = x.