1.

If (1+i)z =(1-i)z conjugated show z =-iz conjugated

Answer»

( 1 + i)Z = (1 - i)z'

Now,

To PROVE ,

z= -z'


Proof:


So,


1 + i in POLAR form can be written as,

√2 (e^(i×pi) / 2)


And,

1- i = √2(e^(-i×pi) / 2)


So,

( 1 +i)z = (1 - i)z'


√2 (e^(i×pi) / 2) z = √2(e^(-i×pi) / 2)z'


z= (e^(-i×pi/2 - i× pi/ 2))z'


z= (e^(-i×pi)) z'


Now,

(e^(-i×pi) = cos (pi) + ISIN (pi)

= -1


So,

z= -z'


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