If (1 + i)z = (1 – i) then prove that z = -
Let z = x + iy
Then,
Now, Given: (1 + i)z = (1 – i)
Therefore,
(1 + i)(x + iy) = (1 – i)(x – iy)
x + iy + xi + i2y = x – iy – xi + i2y
We know that i2 = -1, therefore,
x + iy + ix – y = x – iy – ix – y
2xi + 2yi = 0
x = -y
Now, as x = -y
z = -
Hence, Proved.