Question

If (1+i)z=(1-i)z conjugate then show that z=-iz conjugate

Answer 1

Let z=a+ibz=a+ib. Your condition is equivalent

to a−iba+ib=1+i1−ia−iba+ib=1+i1−i.


But 1+i1−i=(1+i)22=i1+i1−i=(1+i)22=i.

Therefore, a−ib=i(a+ib)a−ib=i(a+ib), which is equivalent