Q25 of 202 Page 171

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.


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