Q. 25

# 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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